deductive reasoning problem solving examples

15 Deductive Reasoning Examples

deductive reasoning examples and definition, explained below

Deductive reasoning is a logical process and type of inference that involves taking a generally true statement and narrowing it down to apply to a specific instance.

It is the opposite of inductive reasoning in which we take a specific piece of information and generalize it.

Here’s how it works:

Sometimes referred to as ‘top-down’ reasoning, or deductive logic, this form of reasoning is extraordinarily common and used implicitly by people on a daily basis.

We use deductive logic to formulate correct and logical arguments, along with their corresponding conclusions.

See more inductive reasoning examples here.

Deductive Reasoning Examples

All bachelors are unmarried men. John is an unmarried man. Therefore, John is a bachelor.

All thrift stores sell used clothes. This shirt is from a thrift store. Therefore, this shirt has been used.

All Canadians have free healthcare. Sarah is Canadian. Sarah has free healthcare.

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

Anyone born in late August to late September is a Virgo. Ashley was born on September 4th. Therefore, Ashley is a Virgo.

To apply to law school you have to take the LSAT (Law School Admissions Test.) Sam is applying to law school. Sam has to take the LSAT.

To get your driver’s license, you have to be at least 16 years old. Jack is not yet 16 years old. Therefore, Jack cannot get his driver’s license.

All kids are required by law to go to public schools at the age of six. Daniel is seven years old. Daniel must go to public school.

Any species that is endangered cannot be hunted. The Pika is an endangered species. Therefore, Pikas cannot be hunted.

All fruits have seeds. Apples are a kind of fruit. Therefore, apples have seeds.

Susan wants to bake a cake, but she doesn’t have any flour. Susan knows that to bake a cake, she needs flour. Since she has no flour, she cannot bake a cake.

See More Examples of Reasoning Here

The Examples Explained

1. john is a bachelor.

This example illustrates deductive reasoning by starting with a general premise, ‘ all bachelors are unmarried men ,’ and then shrinking the statement to apply to the particular or specific instance.

In this case: John is a man, and he is not married; therefore, John is a bachelor. The conclusion is indisputable, unlike in inductive reasoning, where the conclusions are just educated guesses (see: inductive learning in the classroom ).

2. Buying Second-Hand Clothes

The first premise ‘ all thrift stores sell used clothes ,’ is a broad and general statement that applies to any clothes sold at thrift stores. The second premise, ‘this shirt is from a thrift store,’ is where we can clearly see how deductive reasoning ‘deduces’ from a broad claim, or moves from the general to the specific to form a conclusion.

This set of premises work to form a logical conclusion, though it is relevant to mention that deductive reasoning can result in an incorrect or illogical conclusion (even in cases where the premises may themselves be true.)

3. Canada and Free Healthcare

If all Canadians have free healthcare, and Sarah is Canadian, then Sarah must have free healthcare. We don’t really have any way around this because Sarah fits perfectly into the definitive category of ‘Canadians’. The blanket rule, without exceptions, that Canadians have healthcare means that we can conclude with certainty that Sarah gets healthcare for free.

4. Socrates is Mortal

All men are mortal. Socrates is a man. Therefore , Socrates is mortal.

This is the quintessential example of deductive reasoning,(which you have likely encountered if you’ve taken a philosophy course.

This is a case in point of deductive reasoning, and clearly demonstrates the power of deductive logic as a process to arrive at the correct conclusion when the independent premises hold, and are themselves true.

5. Zodiac Signs

While deductive logic goes from the top-down, based on the set of premises given in this example it’s clear that we could induce (or build-up,) to the correct conclusion as well.

Bottom-up reasoning, or arriving at a broad conclusion based on specific premises is known as inductive reasoning, and is in contrast to deductive reasoning.

6. Applying to Law School

To apply to law school you have to take the LSAT (Law School Admissions Test.) Sam is applying to law school. Sam has to take the LSAT.

As it turns out, not all law schools require applicants to take the LSAT in order to be admitted. Standardized tests , in general, are under scrutiny as a form of assessment. The example illustrated above still uses deductive logic correctly, though the conclusion may not be true in each case.

7. Driver’s License

This example utilizes deductive logic to determine whether or not Jack can apply to get his license. In day-to-day life, we do not lay out our thought processes as one would in a philosophy essay, (or in this blog for example). That said, we implicitly use deductive forms of reasoning all the time to arrive at conclusions and shape our beliefs and views.

8. Public School Age Requirement

This example demonstrates the correct use of deductive logic; however, because the first premise is not true in and of itself (other types of education are permitted, i.e., homeschooling, charter schools and private schools) the following conclusion will not hold.

To revise the argument so it is true, we could consider modifying the initial premise to ‘all kids must go to school at the age of six. Daniel is seven years old. Therefore, Daniel must go to school.’

9. Protected Wildlife and Endangered Species

This is a straightforward and successful case that shows precisely how deductive reasoning takes a general statement (namely, any endangered species cannot be hunted.) Subsequently, the scope is narrowed to apply to the particular: Pika’s are endangered; therefore, it is not permissible to hunt Pika’s.

10. Fruits and Seeds

Pretty much all fruits have seeds, and those that appear not to have seeds (like bananas) have been genetically modified, and do produce seeds when they grow naturally in the wild. This example of deductive logic works; still, it’s important to pay close attention to the individual premises because deductive logic is not foolproof and can result in an illogical conclusion.

11. Baking a Cake

Susan may not be able to bake a cake, but at least she’s able to use her deductive reasoning skills to realize it. While it is not always apparent to the person that is utiliizing their deductive skills, Susan started with understanding a general claim about baking cakes—namely, that you need flour.

Subsequently, she realized she had no flour; which then led her to ultimately conclude that she can’t bake a cake (all as a result of her ability to deduce information from a broad claim!)

12. Change of Seasons

Ray lives in Canada, and he knows it gets extremely cold during the winter. Since it is approaching winter, Ray decided to buy a parka to get him through the winter seasons and stay warm.

Assuming that this is not Ray’s first Canadian winter, most likely he knows about Canadian winters, and what to expect weather-wise during that time of year. As a result, Ray is able to deduce (based on the fact that it is nearing winter,) that he’s going to need a new coat to keep warm.

Ray used his deductive logic skills to arrive at the conclusion that he needs a new jacket for winter.

13. Competing in a Triathlon

Noah wants to sign up for a triathlon, but he does not know how to swim. The triathlon involves swimming, so Noah cannot sign up to compete unless he learns how to swim first.

In this case, Noah is able to deduce two important pieces of information by using his deductive reasoning skills: triathlons require swimming, and he needs to know how to swim if he is to compete in the triathlon.

Through the ability to deduct from broader information, Noah is able to form the conclusion that if he is to compete in the triathlon, he has to learn how to swim first.

14. Graduating with a Philosophy Degree

Max needs to pass the logic class in order to graduate from university and earn his philosophy degree. Max failed the course on logic, so Max cannot graduate from university this year.

Since Max is aware of the requirements he needs to fulfill to get his degree, he knows that he has to pass logic to earn his philosophy degree. Max is pulling broad information, (the requirements to earn a degree in philosophy) and applying it to his situation, where it is applicable.

In other words, Max can deduce based on a general set of rules what applies to him specifically, or in the particular.

15. Paying Rent

Morgan wants to move out of her parent’s house, but to do so she has to be able to afford to pay rent. Morgan knows she doesn’t have enough money saved to pay rent, and so she can’t move out of her parent’s house and has to save more.

Based on what she knows of the cost of rent, Morgan is able to determine that she doesn’t have enough money saved to move out of her parent’s house. She furthermore realizes that she has to save more money if she is to move out eventually.

Clearly, Morgan has the ability to deduce general information and apply it to her specific situation to understand what she needs to do to be able to move out. Morgan is using deductive logic to arrive at the conclusion that she has to save more before moving out.

2 thoughts on “15 Deductive Reasoning Examples”

Hi, thanks for the post. Just wanted to tell you about the mistake I found.

Example 1 needs to be corrected. It should go as: All bachelors are unmarried men. John is a bachelor. Therefore, John is an unmarried man.

P is Q and R is Q does not lead to R is P. Instead, P is Q and R is P leads to R is Q. This is how deductive reasoning fits in the logic.

Fixed. Thanks.

Definition of Deductive Reasoning

Examples of deductive reasoning, method of deductive reasoning, approaching deductive reasoning questions, types of deductive reasoning, what is deductive reasoning.

When you switch on a light, you expect it to illuminate the room. This expectation stems from the understanding that all functioning lights, when powered, provide illumination, leading you to deduce that the light you've switched on will do the same.

Similarly, when you plant a seed in fertile soil and water it regularly, you anticipate that it will grow. This is based on the knowledge that seeds, given the right conditions of soil and water, germinate and develop into plants. Thus, the seed you've planted is expected to grow following this logic.

These examples highlight how deductive reasoning is woven into the fabric of our daily lives, guiding us in making informed decisions and understanding the world around us. From everyday choices to academic research, the principles of deductive reasoning underpin our logical thought processes.

This article aims to explore the nuances of deductive reasoning, shedding light on its fundamental aspects and applications.

Deductive reasoning involves deriving a true conclusion from a set of premises using logically sound steps. A conclusion is considered deductively valid when both the conclusion and premises are true.

While the concept may initially appear complex due to unfamiliar terminology, it is actually quite straightforward. Whenever you arrive at a definitive answer based on initial information, you are employing deductive reasoning.

Deductive reasoning can be thought of as drawing specific conclusions from general statements, essentially deriving facts from other facts.

Facts → Facts

General Premises → Specific Conclusions

To illustrate this concept further, let's explore some examples of deductive reasoning.

Mark needs to calculate the area of a circle with a radius of 3 cm. He uses the formula A = π r ^ 2 , leading to A = π × 9 . From the initial premise of knowing the formula for the area of a circle, Mark deduces the area of this specific circle.

Emily observes that all mammals have vertebrae. Seeing a dolphin, she concludes it must have vertebrae because it's a mammal. This conclusion follows logically from the premise that all mammals possess vertebrae.

Tom learns that all prime numbers greater than 2 are odd, and he knows that 17 is a prime number. He concludes 17 must be odd, based on the initial premise about prime numbers. This is an example of deductive reasoning.

These scenarios illustrate deductive reasoning's power in drawing logical conclusions from established facts, whether it's solving mathematical problems, understanding biological traits, or identifying properties of numbers. By applying deductive reasoning, individuals can navigate through complex information with clarity and precision.

Some more everyday examples of deductive reasoning might be:

All birds lay eggs, this creature is a bird - therefore it lays eggs.
All smartphones can access the internet, this device is a smartphone - therefore it can access the internet.
Water boils at 100°C at sea level, the pot of water is at 100°C - therefore, the water is boiling.

However, it's crucial to remember that deductive reasoning relies on the premises being true. If the premises are flawed, the conclusion may not be valid, highlighting the importance of accurate and true premises in deductive reasoning.

Hopefully, you are now familiar with just what deductive reasoning is, but you might be wondering just how you can apply it to different situations.

Well, it would be impossible to cover how to use deductive reasoning in every single possible situation, there are literally infinite! However, it is possible to break it down into a few key tenets that apply to all situations in which deductive reasoning is employed.

In deductive reasoning, it begins with a premise or a set of premises . These are statements believed or assumed to be true, from which conclusions are logically derived. A premise might be a mathematical expression, like 3 x - 5 = 7 , or a factual statement, such as 'all mammals breathe air'.

Premises serve as the foundational truths for deductive reasoning. They act as the starting points from which logical conclusions are drawn.

From these premises, we aim to deduce a conclusion. The critical aspect of deductive reasoning is that each step must logically follow from the last.

For instance, while it's true that all mammals breathe air, it does not logically follow that all air-breathing creatures are mammals. Such a conclusion would constitute an invalid leap in deductive reasoning.

Given the task to find the value of x from the premises,

3 x - 5 = 7 , the logical steps to reach a conclusion about x might proceed as follows:

Step 1. Add 5 to both sides to isolate the term involving x , resulting in 3 x = 12 .

Step 2. Divide both sides by 3 to solve for x , yielding x = 4 .

Verifying the conclusion involves substituting the value of x back into the original equation:

3 × 4 - 5 = 7

12 - 5 = 7 , confirming 7 = 7 .

The equation validates our conclusion, proving the deductive steps taken were logical and correct.

In deductive reasoning, ensuring each step logically follows from the previous is paramount. For example, adding 5 to both sides in step 1 maintains the equation's balance, demonstrating a fundamental principle of deductive reasoning.

When engaging with deductive reasoning problems, it's crucial to avoid assumptions and derive conclusions solely based on the given premises.

Consider this deductive reasoning challenge:

Alice is told that a certain species of fish increases its population by 25% each year in a lake. Starting with 200 fish, she is asked to calculate the fish population in 3 years.

Alice concludes the population will be 390.625 fish in 3 years if the growth trend continues. Is Alice's conclusion a result of deductive reasoning?

Alice's method does not strictly adhere to deductive reasoning principles.

The word "concludes" suggests a calculation based on given data rather than an estimation. Deductive reasoning demands deriving exact conclusions from the premises without assumptions. However, predicting population growth involves applying a mathematical model to given premises, which is a form of deductive reasoning if done without assuming external factors.

To demonstrate deductive reasoning in proving a mathematical property, consider proving that the sum of two even numbers is always even. We define even numbers as those divisible by 2, represented as 2k where k is any integer.

The sum of two even numbers, 2k and 2m, where k and m are integers, can be expressed as 2k + 2m.

Simplifying, we get 2(k + m).

Since k and m are integers, their sum (k + m) is also an integer, indicating the sum is even.

This proof uses deductive reasoning to arrive at a logical conclusion without assumptions.

Employing deductive reasoning, calculate the value of B, where

B = 2 - 2 + 2 - 2 + 2 . . .

First, subtract B from two:

2 - B = 2 - ( 2 - 2 + 2 - 2 + 2 ... )

Expanding the brackets:

2 - B = 2 - 2 + 2 - 2 + 2 ...

Which simplifies to:

2 B = 2 B = 1 2

This series, similar to Grandi's Series, challenges our intuition and demonstrates the power of deductive reasoning in exploring mathematical truths, emphasizing the importance of logical progression in mathematical proofs.

Deductive reasoning comes in several forms, each with its unique approach but fundamentally grounded in logic and simplicity.

A syllogism is a form of reasoning where a conclusion is drawn from two given or assumed propositions (premises). A classic example is: If All M is P , and All S is M , , then All S is P . For instance, if all mammals breathe air, and all dogs are mammals, then all dogs breathe air.

This logical structure is also found in mathematics, such as in transitive relations. If \(a = b\) and \(b = c\), then \(a = c\).

Modus Ponens

Modus Ponens asserts that if a conditional statement (if A, then B) is accepted, and A is true, then B must also be true. For example, if it rains, the ground gets wet. It's raining. Therefore, the ground is wet.

This form of reasoning validates a hypothesis by affirming its antecedent, essentially following a "cause and effect" logic.

Modus Tollens

Conversely, Modus Tollens refutes a hypothesis by denying its consequent. It operates on the principle: if A implies B, and B is false, then A must also be false. An example would be, if it is summer, then the day is long. The day is not long. Therefore, it is not summer.

Modus Tollens is used to logically deduce that a certain condition cannot be true based on the outcome or effect being false, often applied in scientific hypothesis testing and logical arguments.

Deductive reasoning stands as a critical method for drawing reliable conclusions from true premises through a logical and stepwise process. It emphasizes the importance of following a clear, assumption-free path from premise to conclusion to ensure the validity of the reasoning.

However, the reliability of the conclusions hinges on the absence of flawed logic or assumptions. With syllogism, modus ponens, and modus tollens serving as its foundational types, deductive reasoning offers a structured framework for analyzing statements and arriving at conclusions that, when correctly applied, can be considered true with a high degree of certainty. This method is indispensable in fields that require rigorous logical analysis and precise conclusions.

Volume of cylinder calculations: formulas, types, and applications.

Delve into the world of cylinder volume calculations. Learn about types of cylinders, their formulas, including oblique and semicircular, and how to apply them to solve real-world problems efficiently.

What Is Standard Form in Math: Step-by-Step Guide

Uncover the importance of Standard Form in mathematics. Learn to convert numbers and solve linear equations.

Removable Discontinuity: In-Depth Guides with Examples

Explore the concept of removable discontinuity with our comprehensive guides, complete with examples to clarify this fundamental mathematical concept.

Graphs of Common Functions: Linear, Quadratic, Exponential & More

Demystify graphs of common functions from linear to trigonometric. Understand properties, characteristics, and tips for accurate graphing. Enhance mathematical intuition and problem-solving skills.

Deductive Reasoning (Definition + Examples)

At the age of 11 or 12, children enter what famed psychologist Jean Piaget identified as the formal operational stage. While this represents the last of Piaget's stages of cognitive development, it's important to note that development continues in various aspects throughout life, including emotional, moral, and social dimensions. In the formal operational stage, children begin to think abstractly and can apply these abstract thoughts to problem-solving. It's during this stage that they also become acquainted with a process known as deductive reasoning.

Deductive reasoning is a process in which we conclude the world around us. It’s also one of the basic ideas introduced to students learning about logic and how to form an argument. Deductive reasoning can help us discover the truth, but as you’ll see in the video, sometimes this process is done so quickly because it’s obvious.

On this page, I will discuss deductive reasoning, how we use it in everyday life, and how it differs from inductive reasoning. Understanding deductive and inductive reasoning are essential building blocks for understanding how we make sense of the world and how we make decisions.

Top-Down vs. Bottom-Up Logic

When discussing reasoning and logic, two commonly used terms are "top-down" and "bottom-up." These terms refer to the direction or flow of information or reasoning.

Top-Down Logic (Deductive Reasoning) : This method begins with a general statement or hypothesis and examines the possibilities to reach a specific, logical conclusion. It's like starting from a broad perspective and narrowing it down. In essence, if the broader generalization is true, then the specific conclusion must also be proper.
Bottom-Up Logic (Inductive Reasoning) : This is the opposite of the top-down approach. It starts with specific observations and measures, begins to detect patterns and regularities, formulates some tentative hypotheses that we can explore, and finally develops some general conclusions or theories. Instead of starting with a broad generalization, we collect bits of data and form a general conclusion based on those observations.

Understanding Correlation in Reasoning

Another important concept to grasp when discussing reasoning is the idea of correlation. Correlation refers to a relationship or association between two or more variables. When two variables tend to change together consistently, they are said to be correlated.

Correlation and Inductive Reasoning : Often, inductive reasoning involves observing correlations in the real world. For instance, we might observe that when one event happens, another event tends to follow. However, it's crucial to understand that correlation does not imply causation. Just because two variables change together doesn't mean one causes the other. Distinguishing between mere correlation and actual causation is vital for forming accurate conclusions based on observations.

For example, there might be a correlation between ice cream sales and the number of drowning incidents in a given area. While these two variables are correlated (both increase during the summertime), one does not cause the other. Instead, an external factor, like hotter weather, affects both variables.

deductive reasoning and inductive reasoning

What is Deductive Reasoning?

Deductive reasoning, or deduction, is the process of using a group of true premises to draw a conclusion that is also true. This is also known as “top-down logic” because it takes broad statements and uses them to create more narrow statements.

Here’s an example of deductive reasoning.

Premise A says that all dogs are good boys.

Premise B says that Kevin is a dog.

The conclusion that we draw from deductive reasoning says that Kevin is a good boy.

Of course, that example is silly, but it shows how we can use two ideas and deductive reasoning to form an argument or a statement. Other examples of premises like this include “all dogs are mammals” or “every human embryo is made from sperm and an egg.”

Premise A is typically a very broad and general statement. Premise B is a more narrow statement that relates to Premise A. The conclusion states a narrow truth relating to Premise A and Premise B.

Characteristics of deductive reasoning

To start the deductive reasoning process, you must use a statement that we all know to be true. If the statement is not true, or true sometimes , you may still be able to form a conclusion through induction. But to use deductive reasoning, that truth must be as solid as concrete.

It will also have to funnel down to make a more narrow conclusion through entailment. Premises A and B must be related so that Premise C can exist. Let’s go back to our example.

In both Premise A and Premise B, dogs are mentioned. Premise C grabs a conclusion from both premises in a logical, relevant way. When any of these parts of the deduction don’t follow the rules, problems may ensue.

The rules of deductive reasoning are airtight. If you’re not following them, you’re not using deductive reasoning. This may not change the validity of the premises or the conclusions you draw from your premises, but it does change whether or not it falls under the category of deductive reasoning.

If any of the following exist, you might end up coming to a false conclusion:

False premises
Lack of entailment
A narrow truth

False Premises

Let’s go back to the idea that all dogs are good boys. In this case, one can unfortunately argue that not all dogs are good boys. This would automatically make the conclusion untrue. A conclusion is only considered the truth when the premises that precede it are true.

Notice here that we said that the conclusion is untrue. You may argue that Kevin is a good boy, even though not all dogs are. That means that the conclusion is valid. In philosophy, validity and truth are not the same thing.

So while some dogs are good boys, Kevin is a dog, and Kevin is a good boy, this is not a conclusion you can draw through deductive reasoning as ancient philosophers laid it out.

Lack of Entailment

Kevin is a good boy (as discovered by deductive reasoning)

Here’s another problem with deductive reasoning that we run into a lot. For a conclusion to be true, the premises that precede it directly support and lead to the conclusion.

Here’s an example of how failing to use this rule can create a weak conclusion. (Let’s go back to pretending that “all dogs are good boys” is a known fact.)

The conclusion drawn from this is that Kevin has blue eyes.

Kevin could very well have blue eyes, but just because the conclusion is valid doesn’t mean it is true because we have nothing to support the idea that Kevin’s eyes are blue.

Remember, you have to reach this conclusion through entailment. No premise has anything to do with the color of Kevin’s or any dog’s eyes. So we can’t come to that conclusion based on the premises given to us.

Narrow Truth

Think of all of the things that you know as true. Surprisingly, these broad and general facts are not easy to come by. And when they do, they seem too obvious to use in an example.

So deductive reasoning also seems very obvious, and outside of being the basis of forming an argument, it’s not useful in everyday life.

Let’s use another example of deductive reasoning, shall we?

Premise A says that all humans live on land.

Premise B says that Megan is a human.

The conclusion that you would get from deductive reasoning says that Megan lives on land.

Well, yeah. Duh. She’s a human, after all.

Deductive reasoning comes naturally to us. We do it without thinking. To figure out that a human lives on land or that a dog is a mammal is a quick process when you already know that all dogs are mammals and that all humans live on land.

However, due to the nature of deductive reasoning, you need those broad truths to conclude from. A more narrow truth won’t give you much to work with.

Example 1: All humans are mortal. Susan is a human. Susan is mortal.

This is a classic example of deductive reasoning. It starts with an entirely true statement - you can’t poke holes in it or argue against it. (Maybe in a few decades, you can, but not today!) The next statement is also true and ties into the first statement. The conclusion brings both statements together to create a statement that we have now proven is true.

Example 2: Marketing

In everyday life, we don’t always use deductive reasoning using the strict rules of traditional logic. Marketers, for example, may use deductive reasoning to make decisions about how they want to advertise their products to certain groups of customers.

They may use information from focus groups or surveys to create a profile of their products. Let’s say a company that makes cleaning products wants to target single women in their late 20s who are upper-middle-class. They collect information about the demographic and learn that upper-middle-class single women in their late 20s find more valuable products with natural ingredients and are “green.”

Premise 1 is that upper-middle-class women in their 20s find more value in products that have natural ingredients and are “green.”

Premise 2 is that the company’s target audience is upper-middle-class women in their 20s.

The marketers conclude that if they brand their products as “green” and highlight their natural ingredients, their target audience will find more value in their products.

Again, this doesn’t exactly fit the rules of “top-down logic.” Not every upper-middle-class woman particularly cares what is in their cleaning products. And not every upper-middle-class woman is in the company’s target audience. But this is often how we use deductive reasoning to conclude. These conclusions can still be very helpful, even if the conclusions aren’t 100% true.

Example 3: Deductive Reasoning in Math

Deductive reasoning is introduced in math classes to help students understand equations and create proofs. When math teachers discuss deductive reasoning, they usually talk about syllogisms. Syllogisms are a form of deductive reasoning that helps people discover the truth.

Here’s an example.

The sum of any triangle’s three angles is 180 degrees.

You are given a triangle to work with.

You can conclude that the sum of the triangle’s three angles is 180 degrees.

This conclusion will help you move forward when working with the triangle and discovering the length of each side or the measurement of each angle.

Example 4: Deductive Reasoning in Science

Deductions and induction are used to prove hypotheses and support the scientific method. Deduction requires us to examine how closely the premises and the conclusion are related. If the premises are backed by evidence and experiment, the conclusion will likely be true.

In the scientific method, scientists form a hypothesis. They then conduct experiments to see whether that hypothesis is true. With each experiment, they prove the strength of the premises and support their conclusion about whether or not their hypothesis is correct.

Without deductive reasoning, scientists may come to untrue conclusions or accept things that are likely as true things.

Deductive vs inductive reasoning

At the beginning of this video, I mentioned that child psychologist Jean Piaget theorized that children develop the skills of deductive reasoning around 11 or 12 years old. From then on, it’s not exactly something that we think about.

So we’re more likely to conclude things in the opposite direction. We use inductive reasoning to make sense of the world around us. We take a single experience or a few experiences from the past to conclude what might happen in the immediate future or indefinitely.

Inductive reasoning is more prevalent in our everyday lives because it requires a personal experience or a handful of facts. Getting down to the “truth,” especially if you are a philosopher or someone who is especially skilled in logic, is not always an easy thing to do. Plus, deductive reasoning doesn’t usually give us any incentive or confidence to take action. It just helps us build the world.

But I’ll talk more about inductive reasoning in my next video. I’ll break down what inductive reasoning is, the different types of inductive reasoning we use in everyday life, and the problems that come with inductive reasoning.

Have you been listening? Let’s test your knowledge with a quick, three-question quiz on deductive reasoning.

First question:

Is deductive reasoning considered “top-down” or “bottom-up” logic?

“Top-down logic.” It starts with broad truths and goes down to a more narrow conclusion. “Bottom-up logic” is called induction.

Second question:

What can interfere with deduction?

A: False premises

B: Lack of entailment

C: Narrow truth

D: All of the above

All of the above! To arrive at the truth, you must provide true premises that logically lead to the conclusion. This means starting with a very broad truth and making your way down.

Last question: does this “count” as deductive reasoning?

Premise 1: All pigeons are birds.

Premise 2: John is a pigeon.

Conclusion: John is a bird.

Yes, it counts! All of the premises are true and contribute to the conclusion, which is also true.

Inductive Reasoning (Definition + Examples)
Circular Reasoning (29 Examples + How to Avoid)
The Psychology of Long Distance Relationships
Operant Conditioning (Examples + Research)
Beck’s Depression Inventory (BDI Test)

Reference this article:

About The Author

PracticalPie.com is a participant in the Amazon Associates Program. As an Amazon Associate we earn from qualifying purchases.

Youtube Facebook Instagram X/Twitter

Psychology Resources

Developmental

Personality

Relationships

Psychologists

Serial Killers

Psychology Tests

Personality Quiz

Memory Test

Depression test

Type A/B Personality Test

Reset password New user? Sign up

Existing user? Log in

Logical Puzzles

Already have an account? Log in here.

Andrew Hayes

A logical puzzle is a problem that can be solved through deductive reasoning. This page gives a summary of the types of logical puzzles one might come across and the problem-solving techniques used to solve them.

Elimination Grids

Truth tellers and liars, cryptograms, arithmetic puzzles, river crossing puzzle, tour puzzles, battleship puzzles, chess puzzles, k-level thinking, other puzzles.

Main Article: Propositional Logic See Also: Predicate Logic

One of the simplest types of logical puzzles is a syllogism . In this type of puzzle, you are given a set of statements, and you are required to determine some truth from those statements. These types of puzzles can often be solved by applying principles from propositional logic and predicate logic . The following syllogism is from Charles Lutwidge Dodgson, better known under his pen name, Lewis Carroll.

I have a dish of potatoes. The following statements are true: No potatoes of mine, that are new, have been boiled. All my potatoes in this dish are fit to eat. No unboiled potatoes of mine are fit to eat. Are there any new potatoes in this dish? The first and third statements can be connected by a transitive argument. All of the new potatoes are unboiled, and unboiled potatoes aren't fit to eat, so no new potatoes are fit to eat. The second statement can be expressed as the equivalent contrapositive. All of the potatoes in the dish are fit to eat; if there is a potato that is not fit to eat, it isn't in the dish. Then, once again, a transitive argument is applied. New potatoes aren't fit to eat, and inedible potatoes aren't in the dish. Thus, there are no new potatoes in the dish. \(_\square\)

Given below are three statements followed by three conclusions. Take the three statements to be true even if they vary from commonly known facts. Read the statements and decide which conclusions follow logically from the statements.

Statements: 1. All actors are musicians. 2. No musician is a singer. 3. Some singers are dancers.

Conclusions: 1. Some actors are singers. 2. Some dancers are actors. 3. No actor is a singer.

Answer Choices: a) Only conclusion 1 follows. b) Only conclusion 2 follows. c) Only conclusion 3 follows. d) At least 2 of the conclusions follows.

Main Article: Elimination Grids

Some logical puzzles require you to determine the correct pairings for sets of objects. These puzzles can often be solved with the process of elimination, and an elimination grid is an effective tool to apply this process.

An example of an elimination grid

Elimination grids are aligned such that each row represents an object within a set, and each column represents an object to be paired with an object from that set. Check marks and X marks are used to show which objects pair, and which objects do not pair.

Mr. and Mrs. Tan have four children--three boys and a girl-- who each like one of the colors--blue, green, red, yellow-- and one of the letters--P, Q, R, S.

The oldest child likes the letter Q.
The youngest child likes green.
Alfred likes the letter S.
Brenda has an older brother who likes R.
The one who likes blue isn't the oldest.
The one who likes red likes the letter P.
Charles likes yellow.

Based on the above facts, Darius is the \(\text{__________}.\)

Main Article: Truth-Tellers and Liars

A variation on elimination puzzles is a truth-teller and liar puzzle , also known as a knights and knaves puzzle . In this type of puzzle, you are given a set of people and their respective statements, and you are also told that some of the people always tell the truth and some always lie. The goal of the puzzle is to deduce the truth from the given statements.

20\(^\text{th}\) century mathematician Raymond Smullyan popularized these types of puzzles.

You are in a room with three chests. You know at least one has treasure, and if a chest has no treasure, it contains deadly poison.

Each chest has a message on it, but all the messages are lying .

Left chest: "The middle chest has treasure."
Middle chest: "All these chests have treasure."
Right chest: "Only one of these chests has treasure."

Which chests have treasure?

There are two people, A and B , each of whom is either a knight or a knave.

A says, "At least one of us is a knave."

What are A and B ?

\(\) Details and Assumptions:

A knight always tells the truth.
A knave always lies.

Main Article: Cryptograms

A cryptogram is a puzzle in which numerical digits in a number sentence are replaced with characters, and the goal of the puzzle is to determine the values of these characters.

\[ \begin{array} { l l l l l } & &P & P & Q \\ & &P & Q & Q \\ + && Q & Q & Q \\ \hline & & 8 & 7 & 6 \\ \end{array} \]

In the sum shown above, \(P\) and \(Q\) each represent a digit. What is the value of \(P+Q\)?

\[ \overline{EVE} \div \overline{DID} = 0. \overline{TALKTALKTALKTALK\ldots} \]

Given that \(E,V,D,I,T,A,L\) and \(K \) are distinct single digits, let \(\overline{EVE} \) and \( \overline{DID} \) be two coprime 3-digit positive integers and \(\overline{TALK} \) be a 4-digit integer, such that the equation above holds true, where the right hand side is a repeating decimal number.

Find the value of the sum \( \overline{EVE} + \overline{DID} + \overline{TALK} \).

Main Articles: Fill in the Blanks and Operator Search

Arithmetic puzzles contain a series of numbers, operations, and blanks in order, and the object of the puzzle is to fill in the blanks to obtain a desired result.

\[\huge{\Box \times \Box \Box = \Box \Box \Box}\]

Fill the boxes above with the digits \(1,2,3,4,5,6\), with no digit repeated, such that the equation is true.

Enter your answer by concatenating all digits in the order they appear. For example, if the answer is \(1 \times 23 = 456\), enter \(123456\) as your final answer.

Also try its sister problem.

\[ \LARGE{\begin{eqnarray} \boxed{\phantom0} \; + \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; - \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \times \; \boxed{\phantom0}\; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \div \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \end{eqnarray}} \]

Put one of the integers \(1, 2, \ldots , 13\) into each of the boxes, such that twelve of these numbers are used once for each (and one number is not used at all) and all four equations are true.

What is the sum of all possible values of the missing (not used) number?

Main Article: River Crossing Puzzles

In a river crossing puzzle , the goal is to find a way to move a group of people or objects across a river (or some other kind of obstacle), and to do it in the fewest amount of steps or least amount of time.

A famous river crossing problem is Richard Hovasse's bridge and torch problem , written below.

Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in one minute, B in two minutes, C in five minutes, and D in eight minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, can they all get across the bridge in 15 minutes or less? Assume that a solution minimizes the total number of crosses. This gives a total of five crosses--three pair crosses and two solo crosses. Also, assume we always choose the fastest for the solo cross. First, we show that if the two slowest persons (C and D) cross separately, they accumulate a total crossing time of 15. This is done by taking persons A, C, D: D+A+C+A = 8+1+5+1=15. (Here we use A because we know that using A to cross both C and D separately is the most efficient.) But, the time has elapsed and persons A and B are still on the starting side of the bridge and must cross. So it is not possible for the two slowest (C and D) to cross separately. Second, we show that in order for C and D to cross together that they need to cross on the second pair cross: i.e. not C or D, so A and B, must cross together first. Remember our assumption at the beginning states that we should minimize crosses, so we have five crosses--3 pair crossings and 2 single crossings. Assume that C and D cross first. But then C or D must cross back to bring the torch to the other side, so whoever solo-crossed must cross again. Hence, they will cross separately. Also, it is impossible for them to cross together last, since this implies that one of them must have crossed previously, otherwise there would be three persons total on the start side. So, since there are only three choices for the pair crossings and C and D cannot cross first or last, they must cross together on the second, or middle, pair crossing. Putting all this together, A and B must cross first, since we know C and D cannot and we are minimizing crossings. Then, A must cross next, since we assume we should choose the fastest to make the solo cross. Then we are at the second, or middle, pair crossing, so C and D must go. Then we choose to send the fastest back, which is B. A and B are now on the start side and must cross for the last pair crossing. This gives us, B+A+D+B+B = 2+1+8+2+2 = 15. It is possible for all four people to cross in 15 minutes. \(_\square\)

Main Article: Tour Puzzles See Also: Eulerian Path

In a tour puzzle , the goal is to determine the correct path for an object to traverse a graph. These kinds of puzzles can take several forms: chess tours, maze traversals, eulerian paths , and others.

Find the path that leads from the star in the center back to the star in the center. Paths can only go in the direction of an arrow. Image Credit: Eric Fisk Show Solution The solution path is outlined in red below.

Determine a path through the below graph such that each edge is traversed exactly once . Show Solution There are several possible solutions. One possible solution is shown below, with the edges marked in the order they are traversed.

A chess tour is an interesting type of puzzle in its own right, and is explained in detail further down the page.

Main Article: Nonograms

A nonogram is a grid-based puzzle in which a series of numerical clues are given beside a rectangular grid. When the puzzle is completed, a picture is formed in the grid.

The puzzle begins with a series of numbers on the left and above the grid. Each of these numbers represents a consecutive run of shaded spaces in the corresponding row or column. Each consecutive run is separated from other runs by at least one empty space. The puzzle is complete when all of the numbers have been satisfied. The primary technique to solve these puzzles is the process of elimination. If the puzzle is designed correctly, there should be no guesswork required.

Complete the nonogram: Show Solution

One of the many logical puzzles is the Battleship puzzle (sometimes called Bimaru, Yubotu, Solitaire Battleships or Battleship Solitaire). The puzzle is based on the Battleship game.

Solitaire Battleships was invented by Jaime Poniachik in Argentina and was first featured in the magazine Humor & Juegos.

This is an example of a solved Battleship puzzle. The puzzle consists of a 10 × 10 small squares, which contain the following:

1 battleship 4 squares long
2 cruisers 3 squares long each
3 destroyers 2 squares long each
4 submarines 1 square long each.

They can be put horizontally or vertically, but never diagonally. The boats are placed so that no boats touch each other, not even vertically. The numbers beside the row/column indicate the numbers of squares occupied in the row/column, respectively. ⬤ indicates a submarine and ⬛ indicates the body of a ship, while the half circles indicate the beginning/end of a ship.

The goal of the game is to fill in the grid with water or ships.

Main Article: Sudoku

A sudoku is a puzzle on a \(9\times 9\) grid in which each row, column, and smaller square portion contains each of the digits 1 through 9, each no more than once. Each puzzle begins with some of the spaces on the grid filled in. The goal is to fill in the remaining spaces on the puzzle. The puzzle is solved primarily through the process of elimination. No guesswork should be required to solve, and there should be only one solution for any given puzzle.

Solve the sudoku puzzle: Puzzle generated by Open Sky Sudoku Generator Each row should contain the each of the digits 1 through 9 exactly once. The same is true for columns and the smaller \(3\times 3\) squares. Show Solution

Main Article: Chess Puzzles See Also: Reduced Games , Opening Strategies , and Rook Strategies

Chess puzzles take the rules of chess and challenge you to perform certain actions or deduce board states.

One kind of chess puzzle is a chess tour , related to the tour puzzles mentioned in the section above. This kind of puzzle challenges you to develop a tour of a chess piece around the board, applying the rules of how that piece moves.

Dan and Sam play a game on a \(5\times3\) board. Dan places a White Knight on a corner and Sam places a Black Knight on the nearest corner. Each one moves his Knight in his turn to squares that have not been already visited by any of the Knights at any moment of the match.

For example, Dan moves, then Sam, and Dan wants to go to Black Knight's initial square, but he can't, because this square has been occupied earlier.

When someone can't move, he loses. If Dan begins, who will win, assuming both players play optimally?

This is the seventeenth problem of the set Winning Strategies.

Due to its well-defined ruleset, the game of chess affords many different types of puzzles. The problem below shows that you can even deduce whose turn it is from a certain boardstate (or perhaps you cannot).

Whose move is it now?

Main Article: K-Level Thinking See Also: Induction - Introduction

K-level thinking is the name of a kind of assumption in certain logic puzzles. In these types of puzzles, there are a number of actors in a situation, and each of them is perfectly logical in their decision-making. Furthermore, each of these actors is aware that all other actors in the situation are perfectly logical in their decision-making.

Calvin, Zandra, and Eli are students in Mr. Silverman's math class. Mr. Silverman hands each of them a sealed envelope with a number written inside.

He tells them that they each have a positive integer and the sum of the three numbers is 14. They each open their envelope and inspect their own number without seeing the other numbers.

Calvin says,"I know that Zandra and Eli each have a different number." Zandra replies, "I already knew that all three of our numbers were different." After a brief pause Eli finally says, "Ah, now I know what number everyone has!"

What number did each student get?

Format your answer by writing Calvin's number first, then Zandra's number, and finally Eli's number. For example, if Calvin has 8, Zandra has 12, and Eli has 8, the answer would be 8128.

Two logicians must find two distinct integers \(A\) and \(B\) such that they are both between 2 and 100 inclusive, and \(A\) divides \(B\). The first logician knows the sum \( A + B \) and the second logician knows the difference \(B-A\).

Then the following discussion takes place:

Logician 1: I don't know them. Logician 2: I already knew that.

Logician 1: I already know that you are supposed to know that. Logician 2: I think that... I know... that you were about to say that!

Logician 1: I still can't figure out what the two numbers are. Logician 2: Oops! My bad... my previous conclusion was unwarranted. I didn't know that yet!

What are the two numbers?

Enter your answer as a decimal number \(A.B\). \((\)For example, if \(A=23\) and \(B=92\), write \(23.92.)\)

Note: In this problem, the participants are not in a contest on who finds numbers first. If one of them has sufficient information to determine the numbers, he may keep this quiet. Therefore nothing may be inferred from silence. The only information to be used are the explicit declarations in the dialogue.

Of course, the puzzles outlined above aren't the only types of puzzles one might encounter. Below are a few more logical puzzles that are unrelated to the types outlined above.

You are asked to guess an integer between \(1\) and \(N\) inclusive.

Each time you make a guess, you are told either

(a) you are too high, (b) you are too low, or (c) you got it!

You are allowed to guess too high twice and too low twice, but if you have a \(3^\text{rd}\) guess that is too high or a \(3^\text{rd}\) guess that is too low, you are out.

What is the maximum \(N\) for which you are guaranteed to accomplish this?

\(\) Clarification : For example, if you were allowed to guess too high once and too low once, you could guarantee to guess the right answer if \(N=5\), but not for \(N>5\). So, in this case, the answer would be \(5\).

You play a game with a pile of \(N\) gold coins.

You and a friend take turns removing 1, 3, or 6 coins from the pile. The winner is the one who takes the last coin.

For the person that goes first, how many winning strategies are there for \(N < 1000?\)

\(\) Clarification: For \(1 \leq N \leq 999\), for how many values of \(N\) can the first player develop a winning strategy?

Problem Loading...

Note Loading...

Set Loading...

Deductive Reasoning

I. definition.

Deductive reasoning, or deduction, is one of the two basic types of logical inference . A logical inference is a connection from a first statement (a “premise”) to a second statement (“the conclusion”) for which the rules of logic show that if the first statement is true, the second statement should be true.

Specifically, deductions are inferences which must be true—at least according to the rules. If you assume that the premise (first statement) is true, then you can deduce other things that have to be true. These are called deductive conclusions .

Premise : Socrates is a man, and all men are mortal.
Conclusion : Socrates is mortal.
Premise : This dog always barks when someone is at the door, and the dog didn’t bark.
Conclusion : There’s no one at the door.
Premise : Sam goes wherever Ben goes, and Ben went to the library.
Conclusion : Sam also went to the library.

Each of these miniature arguments has two premises (joined by the “and”). These are syllogisms , which provide a model for all deductive reasoning. It is also possible to deduce something from just one statement; but it isn’t very interesting; for example, from the premise “Socrates is a man,” you can certainly deduce that at least one man exists. But most deductions require more than one premise.

You’ll also notice that each premise contains a very general claim–something about “all men” or what the dog “always” does. This is an extremely common feature of deductions: their premises are general and their conclusions are specific.

In each case, the deductive reasoning is valid , meaning that the conclusion has to be true –if the premises are true. The logical relation between premise and conclusion is airtight. However, you always have to be careful with deductive reasoning. Even though the premise and conclusion are connected by an airtight deduction, that doesn’t necessarily mean the conclusion is true. The premises could be faulty, making the conclusions invalid.

Premises are often unreliable. For example, in the real world no dog is 100% reliable, so you can’t be certain that the premise “the dog always barks” is true. Therefore, even though the connection is a logical certainty, the actual truth of each statement has to be verified through the messy, uncertain process of observations and experiments.

There’s another problem with deductive reasoning, which is that deductive conclusions technically don’t add any new information. For example, once you say “All men are mortal, and Socrates is a man,” you’ve already said that Socrates is mortal. That’s why deductions have the power of logical certainty: the conclusion is already contained within the premises. That doesn’t mean deductive reasoning isn’t useful; it is useful for uncovering implications of what you already know—but not so much for developing really new truths.

II. Deductive Reasoning vs. Inductive Reasoning

While deductive reasoning implies logical certainty, inductive reasoning only gives you reasonable probability. In addition, they often move in opposite directions: where deductive reasoning tends to go from general premises to specific conclusions, inductive reasoning often goes the other way—from specific examples to general conclusions.

Examples of inductive reasoning:

Premise: No one has ever lived past the age of 122.
Conclusion: Human beings probably all die sooner or later.
Premise: So far, I’ve never seen someone come to the door without my dog barking.
Conclusion: My dog will probably bark when the next person comes to the door.
Premise: Sam has been following Ben around all day.
Conclusion: Sam will probably go to the library this afternoon when Ben goes.

Induction allows us to take a series of observations (specific premises) and extrapolate from them to new knowledge about what usually happens (general conclusion) or what will probably happen in the future. This seems extremely useful!

III. Quotations about Deductive reasoning

“In the hypothetico-deductive scheme the inferences we draw from a hypothesis are, in a sense, its logical output. If they are true, the hypothesis need not be altered, but correction is obligatory if they are false.” (Peter Medawar)

Peter Medawar wasn’t the clearest writer around, but he won a Nobel Prize for his part in inventing modern organ transplantation. In this quotation, he explains the importance of deductive reasoning in science; science normally advances through incorrect deductions! If we reason logically and our predictions turn out untrue, we know that there is something wrong with our premises, which motivates new theories from which we can deduce new conclusions to test. For example, if the Earth were flat (premise) then you’d be able to reach its edge (conclusion); since we never reach the edge (the conclusion is wrong), it can’t be flat (the premise is untrue) — which means it’s probably a sphere (new theory). In other words, unlike the popular idea that science is a kind of faith, there are no beliefs in real science—except the belief in the scientific method of making and testing hypotheses with reason and evidence.

“An ideally rational progression of thought will finally bring you back to the point of departure where you return aware of the simplicity of genius, with a delightful sensation that you have embraced truth, while actually you have merely embraced your own self.” (Vladimir Nabokov)

In this quote, the novelist Vladimir Nabokov explains his skeptical attitude toward deductive reasoning. He points out what we already discussed–that deductions get their certainty from the fact that they don’t add any new information. Nabokov extends this idea to rationality in general, but in this quotation he seems to be talking specifically about deductive reasoning.

IV. The History and Importance of Deductive Reasoning

Deductive reasoning is more formalized than induction, but its history goes way back before the origins of formal philosophy. It’s possible that the earliest form of deductive reasoning was math. All of mathematics is one big pile of deductions. It starts with some very general rules defining the sequence of whole numbers, and then deduces all sorts of conclusions from there. Math by itself may not teach us about the world; its conclusions are already buried in its premises, and therefore it doesn’t technically produce new information. However, mathematical deductions have progressed so far from their premises that recently it has become a source of new physical theories, such as with ‘string theory’—a trend that bothers many physicists. But in combination with observation and experimentation, math and deduction have always been powerful tool for understanding and manipulating the world. People all over the world have known about this power since prehistoric times.

Ever since then, mathematicians and philosophers have been working out the formal rules for what counts as a valid deduction. Their work allows us to distinguish good deductive reasoning from sloppy or misleading arguments, and forms the backbone of formal logic.

V. Deductive reasoning in Popular Culture

“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” (Sherlock Holmes)

Sherlock Holmes famously uses the word “deduction” a lot. But if you pay attention to his logic, you’ll find that it’s almost always inductive rather than deductive; the word “deduction” is being misused. This quote is a well-known summary of Holmes’s method, and as you can see it describes inductive reasoning rather than deductive reasoning. Theories are general, whereas data is specific; therefore, if you start from data and move to theory, you’re moving from specific to general, which suggests that you’re dealing with induction rather than deduction. The definitive proof, though, is in the fact that Sherlock always comes up with stories that are probable , and often very convincing, but not logically certain . Sherlock Holmes never gives us a deductive syllogism ; he gives only inductive stories.

“It’s not complicated; faster is better. And iPhone 5 downloads fastest on AT&T 4G.”

This is an example of a deductive syllogism in an advertisement. Or, actually, only the two premises are given and the listener is expected to automatically deduce the conclusion. The first premise is a general law: faster is better. The second premise applies the law to a particular situation. And the implied conclusion is obvious: the iPhone is better. This conclusion is so obvious that it doesn’t need to be stated — another demonstration of the fact that deductive conclusions are already contained in the premises, as discussed earlier.

a. Induction

b. Reduction

c. Inference

d. All of the above

a. Probability

b. Logical certainty

c. Evidence

c. Philosophy

c. Deductive reasoning

Home » Deductive Reasoning – Definition, Types and Examples

Deductive Reasoning – Definition, Types and Examples

Table of Contents

Deductive Reasoning

Definition:

Deductive reasoning is a logical process in which a conclusion is drawn from a set of premises or propositions that are assumed or known to be true. The process of deductive reasoning starts with a general statement or premise, and then moves towards a specific conclusion that logically follows from the initial statement. This type of reasoning involves drawing conclusions that are guaranteed to be true, provided that the premises are accurate and the reasoning process is sound.

Steps in Deductive Reasoning

Deductive reasoning typically involves the following steps:

Start with a premise or set of premises: Deductive reasoning begins with one or more premises, which are statements that are assumed to be true.
Identify the logical relationship between the premises: The next step is to determine the logical relationship between the premises, which can be either deductive or inductive.
Apply the rules of deduction: If the logical relationship between the premises is deductive, then the rules of deduction are applied to derive a conclusion that follows necessarily from the premises.
Evaluate the conclusion: The final step is to evaluate the conclusion to determine whether it is valid and sound. A valid conclusion follows necessarily from the premises, while a sound conclusion is both valid and based on true premises.

Types of Deductive Reasoning

There are four types of deductive reasoning that are commonly used in various fields such as mathematics, science, philosophy, and law. Types of Deductive Reasoning are as follows:

Categorical Syllogism

Categorical syllogism is the most common form of deductive reasoning, which involves two premises and a conclusion. These premises and conclusion are based on categorical statements, which are statements that describe relationships between categories. For example, “All men are mortal, and Socrates is a man, therefore Socrates is mortal.”

Hypothetical Syllogism

Hypothetical syllogism is a type of deductive reasoning that involves two premises and a conclusion. These premises and conclusion are based on hypothetical statements, which are statements that describe a conditional relationship between two events or conditions. For example, “If it rains, the ground will be wet. It is raining, therefore the ground is wet.”

Disjunctive Syllogism

Disjunctive syllogism is a type of deductive reasoning that involves two premises and a conclusion. These premises and conclusion are based on disjunctive statements, which are statements that describe a mutually exclusive relationship between two events or conditions. For example, “Either it is sunny outside, or it is raining. It is not sunny, therefore it must be raining.”

Categorical Logic

Categorical logic is a type of deductive reasoning that involves two or more categorical statements, and a conclusion based on those statements. Categorical logic is used to determine the relationship between categories, such as whether two categories are mutually exclusive or overlapping. For example, “All dogs are animals, and some animals are cats. Therefore, some dogs are cats.”

Applications of Deductive Reasoning

Deductive reasoning has numerous applications across various fields, some of which include:

Hypothesis testing: Deductive reasoning is used to formulate hypotheses and test them through empirical evidence. Researchers use deductive reasoning to derive predictions based on theories and test whether these predictions hold true through experiments or surveys.
Data analysis: Deductive reasoning is used to analyze and interpret data in research. Researchers use deductive reasoning to derive logical conclusions based on the data collected and draw inferences about the research question or problem.
Theory building: Deductive reasoning is used to build theoretical frameworks in research. Researchers use deductive reasoning to identify the logical relationships between variables and construct theoretical models that can be tested empirically.
Literature review: Deductive reasoning is used to evaluate and synthesize existing research in a particular field. Researchers use deductive reasoning to identify the logical relationships between different studies and develop a comprehensive understanding of the state of knowledge in the field.
Mathematics: Deductive reasoning is widely used in mathematics to prove theorems and derive logical conclusions based on a set of axioms or assumptions. Mathematical proofs are based on deductive reasoning and are used to validate mathematical theories and concepts.
Science : Deductive reasoning is used in science to formulate hypotheses and test them through experiments. Scientists use deductive reasoning to make predictions based on theories and test whether these predictions hold true through empirical evidence.
Law : Deductive reasoning is a fundamental tool in legal reasoning and argumentation. Legal arguments often involve drawing conclusions from a set of legal precedents or principles, and deductive reasoning is used to derive logical conclusions based on these premises.
Computer Programming: Deductive reasoning is used in computer programming to design algorithms and develop software applications. Programmers use deductive reasoning to identify the logical relationships between different pieces of code and ensure that the program functions as intended.
Philosophy : Deductive reasoning is a foundational principle in philosophy, and is used to derive conclusions based on logical analysis of premises. Philosophers use deductive reasoning to construct arguments and evaluate the soundness of philosophical theories.

Deductive Reasoning Examples

Here are some real-time examples of deductive reasoning that you may encounter in your everyday life:

Weather Forecasting: Weather forecasting involves using deductive reasoning to predict future weather patterns based on past data and current atmospheric conditions. For example, a meteorologist may use deductive reasoning to predict that it will rain tomorrow based on the observation of dark clouds in the sky and the past observation that dark clouds often lead to rain.
Medical Diagnosis: Medical diagnosis often involves using deductive reasoning to identify the underlying cause of a patient’s symptoms. For example, a doctor may use deductive reasoning to diagnose a patient with pneumonia based on the observation of symptoms such as coughing, fever, and difficulty breathing, which are consistent with pneumonia.
Sherlock Holmes’ Investigations: The fictional detective Sherlock Holmes often uses deductive reasoning to solve cases. For example, in “The Adventure of the Speckled Band,” Holmes uses deductive reasoning to identify the culprit by ruling out possible suspects based on the observation of physical evidence and the behavior of the characters involved.
Investment Decisions: Investment decisions often involve using deductive reasoning to analyze financial data and make informed decisions about buying or selling stocks. For example, an investor may use deductive reasoning to decide to buy a stock based on the observation of positive earnings reports and the past observation that positive earnings reports often lead to an increase in the stock price.
Deductive Reasoning Example in Math: The Pythagorean Theorem: if a triangle has sides of lengths a, b, and c, where c is the hypotenuse (the longest side), then a² + b² = c².

When to use Deductive Reasoning

Problem-Solving: Deductive reasoning can be used to solve problems in everyday life, such as determining the cause of a malfunctioning appliance based on observation of its symptoms.
Decision Making: Deductive reasoning can be used to make decisions based on logical analysis of premises. For example, deductive reasoning can be used to determine the most effective marketing strategy for a product based on the analysis of past sales data and consumer behavior
Proving Theorems: Deductive reasoning is widely used in mathematics to prove theorems based on a set of axioms or assumptions.
Legal Reasoning: Legal arguments often involve drawing conclusions from a set of legal precedents or principles, and deductive reasoning is used to derive logical conclusions based on these premises.
Science and Research: Deductive reasoning is used in science to formulate hypotheses and test them through experiments, as well as to analyze and interpret data collected.

How to conduct Deductive Reasoning

Here are the steps to conduct Deductive Reasoning:

Identify the premises: Deductive reasoning starts with a set of premises or assumptions that are known to be true. Identify these premises before starting the reasoning process.
Identify the conclusion: The goal of deductive reasoning is to draw a conclusion based on the premises. Identify the conclusion that you want to draw before starting the reasoning process.
Apply logical rules: Deductive reasoning involves applying logical rules to the premises to derive the conclusion. These logical rules include syllogisms, modus ponens, modus tollens, and other rules of inference.
Evaluate validity: Once you have applied logical rules to the premises, evaluate the validity of the conclusion. A valid conclusion follows logically from the premises, while an invalid conclusion does not.
Test the conclusion: Test the conclusion by comparing it with real-world observations or by testing it through experiments. If the conclusion is supported by evidence, then it is likely to be true.
Revise and refine: If the conclusion is not supported by evidence, revise the premises or apply different logical rules to arrive at a more valid conclusion. Refine the reasoning process until a valid conclusion is reached.

Purpose of Deductive Reasoning

The purpose of deductive reasoning is to draw valid conclusions based on a set of known premises or assumptions. Deductive reasoning is a logical process that is used to derive conclusions based on the application of logical rules to premises. The goal of deductive reasoning is to arrive at a valid conclusion that is logically consistent with the premises.

Advantages of Deductive Reasoning

Here are some advantages of deductive reasoning:

Clear and precise: Deductive reasoning is a clear and precise way to arrive at a conclusion based on a set of known premises or assumptions. It allows for logical analysis of information and can help to eliminate ambiguity and confusion.
Logical consistency: Deductive reasoning ensures that the conclusion is logically consistent with the premises. It helps to ensure that the reasoning process is valid and that the conclusion is trustworthy.
Predictive power: Deductive reasoning can be used to make predictions based on a set of premises. It can help to identify potential outcomes and to develop strategies to achieve desired outcomes.
Efficiency : Deductive reasoning is an efficient way to arrive at a conclusion. It allows for a step-by-step approach that can help to eliminate irrelevant information and focus on the most important facts.
Repeatability : Deductive reasoning can be repeated and verified by others. It provides a framework for logical analysis of information that can be used by others to arrive at the same conclusion.

Limitations of Deductive Reasoning

Here are some limitations of deductive reasoning:

Dependence on premises: Deductive reasoning is dependent on the premises or assumptions that are used. If the premises are incorrect or incomplete, the conclusion will also be incorrect or incomplete.
Limited scope: Deductive reasoning is limited to what is already known or assumed. It cannot be used to discover new information or to generate new hypotheses.
Possibility of errors: Despite being based on logic and rules of inference, deductive reasoning can still be prone to errors. Human error in applying the rules or in identifying the correct premises can lead to incorrect conclusions.
Lack of creativity: Deductive reasoning is a rigid process that follows logical rules. It does not allow for creative thinking or intuition, which may be important in certain situations.
Dependence on consistency: Deductive reasoning is dependent on the consistency of the logical rules and the premises. If there is inconsistency in the rules or the premises, deductive reasoning may not work.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

Research Approach – Types Methods and Examples

Abductive Reasoning – Definition, Types and...

Inductive Reasoning – Definition, Types and Guide

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Algebra (all content)

Course: algebra (all content) > unit 18.

school Campus Bookshelves
menu_book Bookshelves
perm_media Learning Objects
login Login
how_to_reg Request Instructor Account
hub Instructor Commons
Download Page (PDF)
Download Full Book (PDF)
Periodic Table
Physics Constants
Scientific Calculator
Reference & Cite
Tools expand_more
Readability

selected template will load here

This action is not available.

3.4: Inductive and Deductive Reasoning

Last updated
Save as PDF
Page ID 89966

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

Learning Objectives

Students will be able to

Identify and utilize deductive and inductive reasoning

Ask somebody who has a job as to why they have a job and there is a good chance they have a reason or multiple reasons. Most likely they will respond by saying that they need the money for their basic necessities. They may even respond that they just want to keep busy or that their parents told them they had to. The point is that there are reasons.

Definition: Reasoning

Reasoning is the act of drawing a conclusion from assumed fact(s) called premise(s) .

Examples \(\PageIndex{1}\)

Identify the premise(s) and conclusion in each case of reasoning:

a) "Martha wants to buy a new smartphone, so she decides to get a job."

b) The traffic app notifies Pedro that the traffic on Interstate 215 North will cause him to arrive at his destination at 3 p.m., an hour later than he expected. The app also shows that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. Pedro decides to take the Interstate 15 North.

a) The premise is that Martha wants to buy a new smartphone and the conclusion is that she decides to get a job.

b) There are two premises in this example. One, that the traffic on Interstate 215 North will cause Pedro to arrive at his destination at 3 p.m, and the other that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. The conclusion is that Pedro takes the Interstate 15 North.

There are many different forms of reasoning defined by scholars, two of which are defined below.

Definitions: Inductive and Deductive Reasoning

Inductive reasoning: uses a collection of specific instances as premises and uses them to propose a general conclusion .

Deductive reasoning: uses a collection of general statements as premises and uses them to propose a specific conclusion .

Notice carefully how both forms of reasoning have both premises and a conclusion. The important difference between these two types is the nature of the premises and conclusion. Applying these definitions to some examples should illuminate the differences and similarities.

Examples \(\PageIndex{2}\)

Identify the premises and conclusion of the reasoning below. Identify the type of reasoning used and explain your choice.

a) “When I went to the store last week I forgot my purse, and when I went today I forgot my purse. I always forget my purse when I go to the store”

b) “Every day for the past year, a plane flies over my house at 2 p.m. A plane will fly over my house every day at 2 p.m.”

c) "All electronic devices are useful. My cell phone is an electronic device. Therefore, my cell phone is useful."

d) Spicy food makes me teary. Habanero sauce is spicy food. Habanero sauce makes me teary.

a) The premises are:

When I went to the store last week I forgot my purse.
When I went today I forgot my purse.

The conclusion is:

I always forget my purse when I go to the store

This is an example of inductive reasoning because the premises are specific instances, while the conclusion is general.

b) The premise is:

Every day for the past year, a plane flies over my house at 2 p.m
A plane will fly over my house every day at 2 p.m.

c) The premises are:

All electronic devices are useful.
My cell phone is an electronic device.
My cell phone is useful.

d) The premises are:

Spicy food makes me teary.
Habanero sauce is spicy food.
Habanero sauce makes me teary.

This is an example of deductive reasoning because the premises are general statements, while the conclusion is specific.

Scriptwriting

What is Deductive Reasoning? Definition and Examples

What is Deductive Reasoning
What is Abductive Reasoning
What is Inductive Reasoning
Inductive vs Deductive Reasoning
What are Context Clues

I f you’ve ever read a detective story before, you’ve probably heard the term “deductive reasoning,” but what is deductive reasoning and what makes it different from inductive reasoning? We’re going to answer those questions by looking at some deductive reasoning examples from Monty Python and the Holy Grail and Sherlock . By the end, you’ll know how to properly apply deductive reasoning in your writing and daily life.

Deductive Reasoning Definition and Examples

First, let’s define deductive reasoning.

Deductive reasoning, or deductive logic, is used to determine whether premises add up to a sensible conclusion. But for a conclusion to be made, deductions must be tested. We’ll get into some deductive reasoning examples but let’s start with a definition.

DEDUCTIVE REASONING DEFINITION

What is deductive reasoning.

Deductive reasoning is a “top-down” process of understanding whether or not an assumption is true, based on logic and experimentation. Deductions begin with a general assumption, then shrink in scope until a specific determination is made. For example, a general assumption may state that all dogs have eyes; this is a logical premise, but I could argue that I have eyes, therefore I must be a dog, which would prove the deduction to be illogical.

Characteristics of Deductive Reasoning

Top-to-bottom reasoning
Effective for reaching certain conclusions
Not a “foolproof” method

For example, say an angry consortium of villagers intend to burn a witch. They say that since witches float in water, they must be as light as a duck. To test this, the villagers weigh the witch against a duck.

The logic suggests that if the witch and the duck are the same weight, then the woman must be a witch. Sound familiar? That’s because it’s taken from a scene from Monty Python and the Holy Grail . Check out the clip below:

Monty Python Deductive Reasoning Examples

This scene satirizes many of the issues that exist with deductive and inductive reasoning — but it also shows that you can expose these follies for comedic effect. So what is deductive reasoning used for?

Inductive and Deductive Thinking

Inductive vs deductive reasoning.

I know what you’re thinking, “what’s the difference between inductive and deductive reasoning ?” Good question! Deductive and inductive reasoning are opposites — deduction applies a top-to-bottom (general to specific) approach to reasoning whereas induction applies a bottom-to-top (specific to general) approach. This next video explores in further detail the ways in which examples of the two modes are different.

Inductive vs Deductive Reasoning Examples

Here’s another way to think about inductive vs deductive reasoning:

Deductive reasoning starts with a general assumption, it applies logic, then it tests that logic to reach a conclusion. With this type of reasoning, if the premises are true, then the conclusion must be true.

Logically Sound Deductive Reasoning Examples:

All dogs have ears; golden retrievers are dogs, therefore they have ears.
All racing cars must go over 80MPH; the Dodge Charger is a racing car, therefore it can go over 80MPH.
Christmas is always Dec. 25th; today is Dec. 25th, therefore it’s Christmas.

Logically Unsound Deductive Reasoning Examples:

All zebras have stripes; tigers have stripes, therefore tigers are zebras.
Fourth of July always has fireworks; today there were fireworks, therefore it must be the Fourth of July.
Carrots are orange; oranges are orange, therefore oranges are carrots.

Inductive reasoning starts with a specific assumption, then it broadens in scope until it reaches a generalized conclusion. With inductive reasoning, the conclusion may be false even if the premises are true.

Generalized Inductive Reasoning Example:

There are a total of 20 apples and oranges in a basket. I pulled out five; four apples and one orange, therefore there are 16 apples and four oranges in the basket.

Predictive Inductive Reasoning Example:

Most baseball players become coaches. Eduardo is a baseball player, so he’ll become a coach.

Statistical Syllogism Inductive Reasoning Example:

95% of Oxford graduates went on to get PhD’s; Rocky graduated from Oxford, therefore he’s going to get a PhD.

There’s a third type of reasoning called abduction. Abductive reasoning is a predictive inference in which we guess the most likely conclusion given a specific set of premises. Here’s an example:

I arrived home to find the birthday cake crudely eaten. Nobody was home besides my dog. My dog must have eaten the birthday cake.

Deductive Reasoning Examples in Everyday Life

Types of deductive reasoning.

There are three major types of deductive reasoning we can use to test deductions: syllogism, modus ponens, and modus tollens. Let's break these down one at a time.

Syllogism is probably the most simple of the 3 types of deductive reasoning. In simplest terms syllogism states that if A=B and B=C, then A=C. It takes two separate clauses and connects them together. A more creative example would be: a puma is a cat, cats are mammals, therefore pumas are mammals.

Modus Ponens

A modus ponens is when a deduction is presented as a conditional statement, proven by subsequent clauses: the antecedent and consequent. For example: Every player on the Boston Celtics is between the ages of 21 and 31. Jayson Tatum is on the Boston Celtics, therefore he must be between 21 and 31.

Modus Tollens

A modus tollens is the opposite of a modus ponens. Whereas the latter affirms a conditional statement, the former refutes it. For example: The freezing point of water is 32 degrees Fahrenheit. It’s hotter than 32 degrees Fahrenheit, so water will not freeze.

Deductive Reasoning Meaning

Deductive reasoning in storytelling.

In storytelling, deductive reasoning means more than what it was intended to. This type of reasoning has become a carte blanche term for when a character makes any sort of inference. A lot of the time, we say that inferences are deductions when in reality, they’re inductions or abductions.

Sherlock Holmes is a character that appropriately applies deductive thinking to reach logical conclusions. By this, I mean that when Sherlock makes an inference, the premises of the assumption usually add up to the conclusion. Let’s take a look at a clip from the BBC series Sherlock to see how deductive reasoning is used in TV:

Sherlock Deductive Reasoning Examples

It may be a little difficult to hear Sherlock explain deductive reasoning here due to the breakneck speed in which he speaks, but if you listen closely, you’ll hear that all the premises add up to a logical conclusion.

If the inferences were inductive, Sherlock would acknowledge a generalization. If they were abductive, he’d have to suggest probability. But he does neither. Instead, he promises that his inferences are true, and that they must be true because all premises are accounted for.

So what is deductive reasoning? Well, it’s fair to say the deductive reasoning method is used to test the premises of a statement. When used correctly, deductions allow us to see the world in mostly objective sense.

Guy Ritchie's best movies

Want to see some deductions courtesy of Sir Sherlock Holmes? Guy Ritchie's pair of reimagined detective capers with Holmes and Watson are your best bet.

Up Next: Guy Ritchie movies ranked →

Showcase your vision with elegant shot lists and storyboards..

Create robust and customizable shot lists. Upload images to make storyboards and slideshows.

Learn More ➜

Pricing & Plans
Product Updates
Featured On
StudioBinder Partners
The Ultimate Guide to Call Sheets (with FREE Call Sheet Template)
How to Break Down a Script (with FREE Script Breakdown Sheet)
The Only Shot List Template You Need — with Free Download
Managing Your Film Budget Cashflow & PO Log (Free Template)
A Better Film Crew List Template Booking Sheet
Best Storyboard Softwares (with free Storyboard Templates)
Movie Magic Scheduling
Gorilla Software
Storyboard That

A visual medium requires visual methods. Master the art of visual storytelling with our FREE video series on directing and filmmaking techniques.

We’re in a golden age of TV writing and development. More and more people are flocking to the small screen to find daily entertainment. So how can you break put from the pack and get your idea onto the small screen? We’re here to help.

Making It: From Pre-Production to Screen
What is a Freeze Frame — The Best Examples & Why They Work
TV Script Format 101 — Examples of How to Format a TV Script
Best Free Musical Movie Scripts Online (with PDF Downloads)
What is Tragedy — Definition, Examples & Types Explained
What are the 12 Principles of Animation — Ultimate Guide
28 Facebook
1 Pinterest
12 LinkedIn

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

Knowledge Base
Methodology
Inductive vs Deductive Research Approach (with Examples)

Inductive vs Deductive Reasoning | Difference & Examples

Published on 4 May 2022 by Raimo Streefkerk . Revised on 10 October 2022.

The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory .

Inductive reasoning moves from specific observations to broad generalisations , and deductive reasoning the other way around.

Both approaches are used in various types of research , and it’s not uncommon to combine them in one large study.

Inductive research approach, deductive research approach, combining inductive and deductive research, frequently asked questions about inductive vs deductive reasoning.

When there is little to no existing literature on a topic, it is common to perform inductive research because there is no theory to test. The inductive approach consists of three stages:

A low-cost airline flight is delayed
Dogs A and B have fleas
Elephants depend on water to exist
Another 20 flights from low-cost airlines are delayed
All observed dogs have fleas
All observed animals depend on water to exist
Low-cost airlines always have delays
All dogs have fleas
All biological life depends on water to exist

Limitations of an inductive approach

A conclusion drawn on the basis of an inductive method can never be proven, but it can be invalidated.

Example You observe 1,000 flights from low-cost airlines. All of them experience a delay, which is in line with your theory. However, you can never prove that flight 1,001 will also be delayed. Still, the larger your dataset, the more reliable the conclusion.

Prevent plagiarism, run a free check.

When conducting deductive research , you always start with a theory (the result of inductive research). Reasoning deductively means testing these theories. If there is no theory yet, you cannot conduct deductive research.

The deductive research approach consists of four stages:

If passengers fly with a low-cost airline, then they will always experience delays
All pet dogs in my apartment building have fleas
All land mammals depend on water to exist
Collect flight data of low-cost airlines
Test all dogs in the building for fleas
Study all land mammal species to see if they depend on water
5 out of 100 flights of low-cost airlines are not delayed
10 out of 20 dogs didn’t have fleas
All land mammal species depend on water
5 out of 100 flights of low-cost airlines are not delayed = reject hypothesis
10 out of 20 dogs didn’t have fleas = reject hypothesis
All land mammal species depend on water = support hypothesis

Limitations of a deductive approach

The conclusions of deductive reasoning can only be true if all the premises set in the inductive study are true and the terms are clear.

All dogs have fleas (premise)
Benno is a dog (premise)
Benno has fleas (conclusion)

Many scientists conducting a larger research project begin with an inductive study (developing a theory). The inductive study is followed up with deductive research to confirm or invalidate the conclusion.

In the examples above, the conclusion (theory) of the inductive study is also used as a starting point for the deductive study.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

Streefkerk, R. (2022, October 10). Inductive vs Deductive Reasoning | Difference & Examples. Scribbr. Retrieved 6 May 2024, from https://www.scribbr.co.uk/research-methods/inductive-vs-deductive-reasoning/

Is this article helpful?

Raimo Streefkerk

Other students also liked, inductive reasoning | types, examples, explanation, what is deductive reasoning | explanation & examples, a quick guide to experimental design | 5 steps & examples.

Deductive reasoning test: Guidelines & Practice Examples

Deductive reasoning test is among the most prevalent aptitude test for pre-employment assessment. Deductive reasoning test measures a candidate’s abilities to make logical deductions for problem-solving. Through the test, the candidates can usually demonstrate themselves to possess potential good qualities such as analytical thinking, good decision-making skill, and a problem-solving mindset.

Therefore, you need to thoroughly prepare for the deductive reasoning test, especially if you are aiming at a high-level management position. The better the result of the test is, the higher chance for you to be invited to the interview round.

In this article, we’ll give you a comprehensive guide on Deductive Reasoning tests, including their definition, question types, typical test providers, and a series of practice tests.

Table of Contents

What is a deductive reasoning test?

Deductive reasoning test is an aptitude test that aims to evaluate a candidate’s ability to make logical deductions – in other words, the ability to formulate a conclusion by analyzing , interpreting , and c onnecting the general facts and data .

Deductive Reasoning questions can be divided into three common types:

Syllogism question: Determine whether a set of premises could lead to the given conclusions.
Ordering and arrangement question: Order and arrange subjects into correct positions based on given conditions.
Grouping question: Select, distribute, or categorize the subjects into groups based on certain conditions.

Companies and employers in various industries use psychometric tests to assess Deductive Reasoning skills (and Logical Reasoning skills) as this skill is fundamental to decision-making ability and analytical thinking skills. Most companies demand this as a core competence from all candidates, especially in managerial positions, which require a lot of strategic thinking and decision-making process.

Syllogism question

A syllogism question presents you with two or more general statements (premises), and specific conclusions. You must use logical deduction skills to determine whether the premises can lead to the provided conclusions . Syllogism question is one of the most classic question forms in deductive reasoning tests.

The format of syllogism questions consists of two parts:

Premises is the first part – the ground rules and the relationships between the subjects.
Conclusion(s) is the second part – the statement to be determined whether it can be derived from the premises using logical deductions. You could be asked to validate one to three conclusions or to choose the True/False conclusion among the given ones.

Source: MConsultingPrep

KEY TAKEAWAYS

A common strategy to approach this question type is to interpret the premises into a visualized logic model called Euler Diagram . This tool helps test takers easily spot the relationships among subjects and avoid choosing false conclusions (fallacy).

Here is an example of a syllogism question:

Statements:

Some berries are red.

Some grapes are green.

All grapes are berries.

Which conclusion is true based on the given statement?

~Br: Berries

~Grp: Grapes

~Grn: Green

1. Analyzing the statements:

Some berries are red. ⇒ Br ∩ R

Some grapes are green. ⇒ Grp ∩ Grn

All grapes are berries. ⇒ Grp ⊂ Br

Based on the above analysis, we can draw the Euler Diagram

Guiding answer:

Some grapes are red. ⇒ Grp ∩ R

Based on the diagram, we can see that Grape and Red can either intersect with each other or not; therefore, we do not have enough information to reach this conclusion ⇒ Eliminate.

Some berries are green. ⇒ Br ∩ Grn

Based on the diagram, we can see that: a Grape is always a Berries; therefore, there are always some green grapes that are also berries ⇒ Conclusion is definitely true.

No berry is green. ⇒ Br ∩ Grn

Similarly, we can see that there are always some green grapes which are also berries ⇒ “No berry is green” can never happen ⇒ Conclusion is definitely false ⇒ Eliminate.

All berries are red. ⇒ Br ⊂ R

Based on the diagram, we can see that Berry and Red can either partly intersect with each other or include each other; therefore, we do not have enough information to reach this conclusion ⇒ Eliminate.

Ordering and arrangement question

Ordering and arrangement questions require you to use your logical deduction skills to order and arrange the subjects into their positions , then choose the correct answer based on the relational positions of the subject. Ordering and arrangement is the most common question type in deductive reasoning tests.

In this question type, all questions come with a scenario and a set of rules provided in the questions; however, the task to be done can be varied from multiple-choice format like most tests or in a gamified interactive format.

Ordering and arrangement questions can be divided into four sub-categories, which are:

Seat arrangement

Blood Relations

Now let’s dive deeper into each type of Ordering & Arrangement question.

Test takers are required to arrange subjects into positions in geometrical order(s) . For some advanced questions, one may have to deal with multiple arrangements and/or some non-arrangement conditions.

To solve a seat arrangement question, test takers need to be able to identify and visualize the geometrical arrangement given in the questions. Then, they have to use logical deduction to transform the condition into relational positions of the subjects.

Here is an example of a seat arrangement question:

Five dishes – Biscuits, Curries, Frankie, Kababs, and Pasta are written in a row on the menu.

1. Biscuits is written next to Curries. 2. Frankie is written next to Kababs. 3. Kababs is neither to the immediate right nor to the immediate left of Pasta, which is on the left end of the menu. 4. Frankie is in the second position from the right. 5. Biscuits is to the right of Curries and Pasta. 6. Biscuits and Frankie are next to each other.

In which position Biscuits is written? A. Between Curries and Kababs B. Between Curries and Frankie C. Between Pasta and Kababs D. Between Frankie and Pasta E. None of the above

Correct answer: B

Explanation:

From clue (1) and (2), we get two pairs of dishes:

[Biscuits-Curries]; [Frankie-Kababs]

From clue (3), we get the position of Pasta:

Pasta _ _ _ _

Kababs is neither to the immediate right nor to the immediate left of Pasta, then Kababs can be any position except for the first and second one.

From clue (4), we get the position of Frankie:

Pasta _ _ Frankie _

From clues (5) and (1), we get the positions of Biscuits and Curries:

Pasta Curries Biscuits Frankie _

The last empty position should be Kababs.

The final seating arrangement will be as follows (at the end of the page)

Therefore, Biscuits is between Curries and Frankie.

The tasks for this type are varied as follows:

Find mutual time slot(s) for the subjects.
Place the subjects on the timetable or calendar.
Figure out the schedule of a specific subject.

To solve a scheduling question, test takers must analyze the given conditions to place the subjects into suitable slots on the timetable or calendar . For the traditional multiple-choice test, you may need to draw the timetable on a piece of paper or in your mind. On the other hand, the interactive test will provide you with the timetable, so you only have to place the subjects in the correct positions.

Here is an example of a Scheduling question:

Five dishes — A, B, C, D, and E, each of them is served on five different days from Monday to Friday, one after another, though not necessarily in the same order. Five dishes are served to five customers Archer, Brooks, Carter, Fletcher, and Graham. Further information is given as follows:

Archer is served with B but not on Thursday or Friday. Brooks is served with A on Wednesday. C or D are not served for Carter. Carter is served on Monday. Which of the following statements is TRUE?

A. Either C or E is served for Fletcher B. D is served on Monday C. E is served for Graham D. D can be served for Graham None of the above

Correct answer: D

We have three entities in the question:

Names of dishes: A, B, C, D, and E
Time frame from Monday to Friday
Names of five customers: Archer, Brooks, Carter, Fletcher, and Graham

Using the four clues we get the following pairings:

[Archer — B — Not Thursday or Friday]

[Brooks — A — Wednesday]

[Carter —Not C or D — Monday]

This leaves Fletcher and Graham to be served with either C or D and either on Thursday or Friday.

Put them together to get the following arrangement:

Ranking questions share certain similarities with seat arrangement questions – it is about putting the subjects in the right spot in a hierarchical order . The noticeable difference in this is that the question mainly concerns only the higher-to-lower type of arrangement . Therefore, it is easier to draw the base diagram than seat arrangement questions.

The solving steps of ranking questions are similar to seat arrangement – starting with drawing the ordering visualization, then interpreting the conditions to put the subjects in their correct positions.

Here is an example of a Ranking question

Paris, Manhattan, Nanno, Oswell, Quinn, and Langston are cousins. All of them have birthdays on the same date, but none of them is the same age.

(i) The youngest is 17 years old.

(ii) Quinn is the eldest and is 22 years old.

(iii) Langston is somewhere between Manhattan and Oswell in age.

(iv) Paris is elder to Manhattan.

(v) Nanno is older than Oswell.

If Nanno is 19 years old, which of the following must be FALSE?

A. Paris is 21 years old B. Oswell is 18 years old C. Nanno is a year older than Langston D. Manhattan is three years older than Oswell

We will break down each premise and build a reaction tracker (the final result is at the end of the page)

(ii) Quinn is the eldest

⇒ Scenario 1: Manhattan < Langston < Oswell

⇒ Scenario 2: Oswell < Langston < Manhattan

⇒ Scenario 1: Manhattan < Langston < Oswell < Paris

⇒ Scenario 2: Oswell < Langston < Manhattan < Paris

Based on the reaction tracker, we can see that there can be only two people younger than Nanno ⇒ Scenario 1 is not plausible.

Since Nanno is 19 and older than Oswell, combined with Scenario 2, we have the complete reaction trackers as in the image

Based on the tracker, we can see that only the statement “Oswell is 18 years old” does not follow the results of reaction trackers.

Blood relations

The blood relations question, also known as the family-tree question, is the arrangement question based on people’s relationships in a family . A blood relations question can involve around 3 to 5 generations , and your task would normally identify the relationship between two people.

It is a complex type of ordering and arrangement question; therefore, it is used to determine the top-tier percentile of candidates (around 10-15%). On the bright side, this question type does not densely appear in the aptitude – so only if you aim to be in this percentile rank, should you practice this question type.

The key to solving this type of question is that you need to know how to interpret the people’s relationships in the family tree – in particular, for each type of relationship, how should you place the people in the family tree accordingly.

To illustrate, let’s look at this example family tree

We have Anne and Alex. Alex is the fourth generation of the family, while Anne is the third generation. They belong to two separate branches of the family tree. Anne, therefore, is Alex’s (distant) aunt, and Alex is Anne’s (distant) niece/nephew.

Grouping question

In the Grouping question, you will be asked to select, divide or match the subjects into subgroups based on the given scenario and set of rules. You must choose the correct answer based on how the groups are formed or how the subjects are distributed into the sub-categories

Among the three common types of deductive questions, many different test providers use grouping less frequently. SHL is the test provider that still includes this type in their Deductive Reasoning Test; therefore, if you will have to take the SHL Test, grouping questions still needs the right amount of attention and preparation.

To solve the grouping questions, you should follow these steps:

Identify the groups/categories and their corresponding conditional statements.
Draw a table/diagram to illustrate the groups
Put each subject into the suitable group one by one using the given conditional statements.
If there are multiple situations arise, draw different diagrams for each situation – then eliminate the situations that conflict with the given conditions.

Here is an example of a grouping question

A farmer wants to raise a hen, a cat, a dog, a bee colony, a goat, and a bear. There are three areas (A, B, C in order), and each can contain 2 creatures.

A bee colony cannot stay with anything

If an area has a dog, then there will be no cat

A goat must stay with the hen

A bear must stay 1 area away from the hen

The areas that don’t have the bee colony must contain 2 creatures

If the farmer keeps the bee colony and the hen if any of these animals are also chosen to stay, which one has no choice but to be in either area A or C?

A. Cat B. Dog C. Goat D. Bear E. Bee

If the Hen stays in B, the bear cannot stay, and every other animal must stay in either A or C, depending on the position of the bee colony.

If the Hen stays in either A or C, and the bees stay in B, every animal must stay in A or C.

If the Hen stays in either A or C and the bees don’t stay in B, every animal can stay in B, but the bear.

Therefore, in every case, the bear can only stay in either A or C, or not stay at all.

Two essential skills to crack deductive reasoning test

To ace your deductive reasoning test, you need to practice them in advance. T here are two basic skills to practice for the deductive reasoning test.

Skill 1: Make a diagrammatic logic model from the question

This is one of the fundamental skills to solve Deductive Reasoning puzzles.. For this skill, you must be able to follow these steps:

Identify the question types to determine which strategies to approach the questions
Identify the subjects and the set of rules that defines their relationships.
Separately interpret each premise (or condition) into the correspondent logic model(s). DO NOT ATTEMPT TO SOLVE ALL PREMISES/CONDITIONS AT ONCE . Each condition/premise has different logic models, so you should look into each question and figure out their logic model.

Skill 2: Interpret the diagram to identify the subjects’ relationship

Using the similar logic that you use to build the diagram, you can now examine each choice of the questions, following these steps:

Identify the subjects to be examined in the diagram
Look at their position on the diagram and name the correspondent relationship to them
Cross-check with the choice given in the question to determine whether it is true or false

For different test providers, the questions could have either ONLY ONE correct answer or multiple correct answers. In addition, for a scenario and set of conditions, the number of questions can range from one to three.

Note: All initial rules or conditions are applied to all the questions given after that. However, sometimes a particular question might introduce new input . Hence, students are expected to consider each question separately from the other questions.

Common test providers

Deductive reasoning exists in different kinds of tests – it can be an independent deductive reasoning test, a general logical reasoning test, or be assessed through other skills tests such as verbal reasoning or numerical reasoning. Here are some of the most popular test providers for the deductive reasoning test.

SHL is one of the most prominent pre-employment test providers in the market. SHL Deductive Reasoning comes in two types of types: SHL Standard Multiple Choice and SHL Interactive Verify Test.

SHL Standard Multiple Choice: This test format consists of 18 multiple-choice questions and lasts for 20 minutes . The question ranges from syllogism, ordering & arrangement, and grouping.

Scheduling question from SHL Deductive Reasoning test (Standard Multiple-choice)

SHL Interactive Verify Test: The test is an innovative way to make the assessment process more engaging. It lasts for 12 minutes and contains 18 interactive questions . Candidates will have to drag, drop, and click on the objects to schedule on a calendar. place rankings based on the given condition or give more.

Seat arrangement question from SHL Deductive Reasoning test (Interactive Verify)

Talogy (formerly known as CUBIKs)

Talogy (Cubiks) was established in 1946 with the mission of using assessments to help young adults join the workforce after a period of work turmoil. Throughout its 70-year history, Talogy has helped to solve talent challenges for numerous companies worldwide.

Talogy does not have a separate test for Deductive Reasoning – this skill is tested in the Verbal Section of the Intermediate CUBIKs test. The intermediate version has 24 questions in 4 minutes , mixing word analogy, syllogism, and short reading comprehension questions.

Here is an example of a Syllogism question in the test

Syllogism question from the Verbal Section of CUBIK – LOGIK Intermediate Test

Kenexa, a child company of IBM, offers employment and retention services. This covers recruitment process outsourcing onboarding tools, employee assessment, abilities assessment for potential candidates, and Kenexa Interview Builder.

The IBM Kenexa Deductive Reasoning test contains 20 questions – all in the form of seat arrangement questions. The test is untimed ; however, you still need to finish the test in the shortest time possible since the completion time will be recorded and considered during the recruitment process.

Key tips to pass the deductive reasoning test

Practice with various types of questions.

A deductive reasoning test covers a lot of different question types, as mentioned above. Each type has a different solving approach. Therefore, not only should you know how to solve every type of question, but you also have to be familiar with them as well, especially when you are not sure which test providers you would take the test from.

Our Deductive Reasoning Test Package includes over 240 questions that cover all of the common question types: Syllogism, Order & Arrangement, and Grouping.

One minute on one question only

A deductive reasoning test requires one person to apply logic models to make sense of the question; nonetheless, to visualize complex logic models while analyzing the questions under time pressure could be dreadful. You should always bring a pen and a note (at least a draft paper) to draw and note down the diagram and information about the question. In this way, your mind is relieved and focuses more on the process of solving a Deductive Reasoning question.

Apply deductive reasoning in real life

A deductive reasoning test could be a tool for employers to assess your ability, but at the end of the day, what an employer looks for is how you use deductive reasoning in a real work situation. Start with solving your daily issues with fact-based analysis. From scheduling a dinner out with your loved one on a busy week or which new iPhone is suitable for you – there is a lot of space to practice deductive reasoning.

Example: If you want to choose whether to buy an iPhone 13 or an iPhone 14, firstly, you would need to establish a set of conditions (or your criteria) for choosing a phone (e.g.: the features, the price, the color, etc.), then you match the characteristics of each phone to the set of conditions to see which one have more matches. This process is how you make logical deductions to reach a conclusion.

Scoring in the McKinsey PSG/Digital Assessment

The scoring mechanism in the McKinsey Digital Assessment

Aptitude Test Package

Simulating most common test publishers, this package provides you with 1400+ numerical, verbal and logical reasoning questions. Ace the aptitude test with our practical study guides tailored to each question type.

Preparing for deductive reasoning tests is daunting if you have no idea what skills to target and what questions you’ll have.

Deductive reasoning is considered one type of logical thinking that involves the process of reaching a specific conclusion from a given general idea.

Find out how hard a deductive reasoning test can be, and what you need to prepare for the test in this article.

School Guide
Mathematics
Number System and Arithmetic
Trigonometry
Probability
Mensuration
Maths Formulas
Class 8 Maths Notes
Class 9 Maths Notes
Class 10 Maths Notes
Class 11 Maths Notes
Class 12 Maths Notes
Quantitative Reasoning in GRE General
Non Verbal Reasoning : Paper Cutting
Case Based Reasoning - Overview
SSC Reasoning Practice Set -2
Inductive Reasoning | Definition, Types, & Examples
Adv | reasoning 8 - TCS | Question 4
Rule Detection : Non Verbal Reasoning
Making Judgements: Reasoning Questions
Adv | Reasoning set 9 - TCS | Question 5
ML | Case Based Reasoning (CBR) Classifier
Adv | Reasoning set 9 - TCS | Question 8
Adv | reasoning set 1 tcs | Question 1
Reasoning | set 3 - TCS | Question 3
Adv | Reasoning set 6 - TCS | Question 1
Verbal Reasoning Questions and Answers
Reasoning | set 8 - TCS | Question 1
Reasoning | set 1 - TCS | Question 4
Reasoning | set 6 - TCS | Question 2
Adv | reasoning set 1 tcs | Question 6

Deductive Reasoning

Deductive reasoning is a basic aspect of logical thinking. It allows individuals to draw valid conclusions based on given premises. It involves applying established rules or patterns to reach logical outcomes. Deductive reasoning helps us in solving puzzles to making decisions in various aspects of daily life.

In this article, we will explore the concept of deductive reasoning, its importance, types, and practical applications.

Table of Content

What is Deductive Reasoning?

Types of Deductive Reasoning

How to Solve Deductive Reasoning?

Deductive Reasoning vs Inductive Reasoning

Application of Deductive Reasoning

Deductive reasoning solved examples.

Deductive reasoning is a logical process where one draws a specific conclusion from a general premise. It involves using general principles or accepted truths to reach a specific conclusion.

For example, if the premise is “All birds have wings,” and the specific observation is “Robins are birds,” then deducing that “Robins have wings” is a logical conclusion.

In deductive reasoning, the conclusion is necessarily true if the premises are true.
It follows a top-down approach, starting with general principles and applying them to specific situations to derive conclusions.
Deductive reasoning is often used in formal logic, where the validity of arguments is assessed based on the structure of the reasoning rather than the content.
It helps in making predictions and solving puzzles by systematically eliminating possibilities until only one logical solution remains.

Different types of deductive reasoning are based on the premises and the kind of relationship across the premises.

The three different types of deductive reasoning are

Modus ponens
Modus tollens

These three types of deductive reasoning provide structured methods for drawing logical conclusions based on given premises.

Syllogism is a form of deductive reasoning that involves drawing conclusions from two premises, typically in the form of a major premise, a minor premise, and a conclusion. It follows a logical structure where if the premises are true, the conclusion must also be true.

In syllogism, the major premise establishes a general statement, the minor premise provides a specific instance, and the conclusion follows logically from these premises. For example:

Major premise: All humans are mortal.
Minor premise: Socrates is a human.
Conclusion: Therefore, Socrates is mortal.

Modus Ponens

Modus Ponens is a deductive reasoning pattern that asserts the truth of a conclusion if the premises are true. It follows the format of “if P, then Q; P; therefore, Q.”

In Modus Ponens, if the first premise (conditional statement) is true and the second premise (antecedent) is also true, then the conclusion (consequent) must logically follow. For example:

Premise 1: If it rains, then the streets will be wet.
Premise 2: It is raining.
Conclusion: Therefore, the streets are wet.

Modus Tollens

Modus Tollens is another deductive reasoning pattern that denies the truth of the consequent if the premises are true. It follows the format of “if P, then Q; not Q; therefore, not P.”

In Modus Tollens, if the first premise (conditional statement) is true and the consequent is not true, then the antecedent must also be false. For example:

Premise 1: If it is a weekday, then John goes to work.
Premise 2: John is not going to work.
Conclusion: Therefore, it is not a weekday.

How to Solve Deductive Reasoning ?

To solve deductive reasoning problems, we follow these simple steps:

Step 1: Carefully read and understand the given premises or statements.

Step 2 : Look for logical patterns or relationships between the premises and the conclusion.

Step 3 : Use deductive reasoning rules like syllogism, modus ponens, or modus tollens to derive conclusions.

Step 4: Ensure that the conclusions logically follow from the given premises.

Step 5: Explore different possibilities and scenarios to verify the validity of the conclusions.

Here are the differences between deductive reasoning and inductive reasoning:

Deductive reasoning plays an important role in various fields, heling in logical thinking, problem-solving, and decision-making processes. Here are some of the applications of Deductive Reasoning :

Deductive reasoning helps break down complex problems into manageable parts and derive logical solutions.
It is widely used in geometry, algebra, and logic to prove theorems and solve mathematical problems.
Scientists use deductive reasoning to formulate hypotheses, design experiments, and draw conclusions based on empirical evidence.
Deductive reasoning is fundamental in philosophical arguments and debates, guiding logical analysis and critical thinking.
Lawyers use deductive reasoning to build cases, establish arguments, and interpret laws and regulations.
Programmers apply deductive reasoning to develop algorithms, write code, and debug software.
Teachers use deductive reasoning to design lesson plans, explain concepts, and assess students’ understanding.

Example 1: Identify the conclusion drawn from the following syllogism: “All mammals are warm-blooded. Elephants are mammals. Therefore, elephants are warm-blooded.”

Conclusion drawn from the syllogism is that elephants are warm-blooded. This conclusion follows logically from the two premises provided: “All mammals are warm-blooded” and “Elephants are mammals.” Since elephants fall within the category of mammals, they inherit the characteristic of being warm-blooded.

Example 2: Apply modus ponens to the following premises: “If it rains, then the ground is wet. It is raining.” What conclusion can be drawn?

Modus ponens asserts that if the first statement is true and the second statement follows from it, then the conclusion is true. In this case, the premises are “If it rains, then the ground is wet” (first statement) and “It is raining” (second statement). Therefore, the conclusion drawn is “Therefore, the ground is wet.”

Example 3: Utilize modus tollens with the given premises: “If the battery is dead, then the car won’t start. The car starts.” What conclusion can be derived?

Modus tollens asserts that if the second statement is false and the first statement implies it, then the first statement must also be false. In this scenario, the premises are “If the battery is dead, then the car won’t start” (first statement) and “The car starts” (second statement). Therefore, the conclusion drawn is “Therefore, the battery is not dead.”

Example 4: Analyze the following syllogism: “All A are B. All B are C. Therefore, all A are C.” Is the conclusion valid? Why or why not?

Conclusion “Therefore, all A are C” is valid. It follows the logical structure of the syllogism, where if all A are B and all B are C, then it logically follows that all A are C. This type of deductive reasoning is known as transitive reasoning.

FAQs on Deductive Reasoning

What is deductive reasoning.

Deductive reasoning involves drawing logical conclusions from premises that are assumed to be true.

How does deductive reasoning differ from inductive reasoning?

Deductive reasoning moves from general principles to specific conclusions, while inductive reasoning moves from specific observations to general principles.

What are some types of deductive reasoning?

Types of deductive reasoning include syllogism, modus ponens, and modus tollens, where conclusions are drawn based on logical rules.

Why is deductive reasoning important?

Deductive reasoning ensures the validity of logical arguments and helps make sound conclusions based on known premises.

What are the characteristics of deductive reasoning?

Deductive reasoning produces certain conclusions if the premises are true and follows a top-down approach.

How can deductive reasoning be applied in everyday life?

It can be used in problem-solving, decision-making, and logical analysis of various situations and arguments.

Please Login to comment...

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Analytical Reasoning

This is important. Starting with the August 2024 LSAT , the multiple-choice portion of the test will consist of two scored Logical Reasoning sections and one scored Reading Comprehension section, plus one unscored section of either Logical Reasoning or Reading Comprehension.

For the remaining tests in the current 2023-2024 testing cycle, up to and including the June 2024 test, the multiple-choice portion of the test will continue to include one Logical Reasoning section, one Reading Comprehension section, and one Analytical Reasoning section, plus one unscored section that could be any of the three section types.

Analytical Reasoning (AR) questions are designed to assess your ability to consider a group of facts and rules, and, given those facts and rules, determine what could or must be true. AR questions appear in sets, with each set based on a single passage. The passage used for each set of questions describes a scenario involving ordering relationships or grouping relationships, or a combination of both types of relationships. Examples might include scheduling employees for work shifts, assigning instructors to class sections, ordering tasks according to priority, and distributing grants for projects.

The specific scenarios associated with these questions are usually unrelated to law, since they are intended to be accessible to a wide range of test takers. However, AR questions test skills that closely parallel those involved in determining what could or must be the case given a set of regulations, the terms of a contract, or the facts of a legal case in relation to the law.

In this sense, AR questions reflect the kinds of detailed analyses of relationships and sets of constraints that a law student must perform in legal problem solving. For example, an AR passage might describe six diplomats being seated around a table, following certain rules of protocol as to who can sit where. You might then be asked to answer questions about the logical implications of the rules as they apply to the scenario. For example, you might be asked who can sit between diplomats X and Y, or who cannot sit next to X if W sits next to Y.

Similarly, in law school you might be asked to analyze a scenario involving a set of particular circumstances and a set of rules that apply to the scenario—rules such as constitutional provisions, statutes, administrative codes, or prior rulings that have been upheld. You might then be asked to determine the legal options in the scenario: what is required given the scenario, what is permissible given the scenario, and what is prohibited given the scenario. Or you might be asked to develop a “theory” for the case: when faced with an incomplete set of facts about the case, you must fill in the picture based on what is implied by the facts that are known. Sometimes you will be asked to assess the impact of hypotheticals that add new information (as in the example above: If W sits next to Y, then who cannot sit next to X.).

AR questions test a range of deductive reasoning skills:

Comprehending the basic structure of a set of relationships by determining a complete solution to the problem posed (for example, an acceptable seating arrangement of all six diplomats around a table)
Reasoning with conditional (“if-then”) statements
Inferring what could be true or must be true from given facts and rules
Inferring what could be true or must be true from given facts and rules together with new information presented in hypotheticals
Recognizing when two statements are logically equivalent in context

You don’t need any formal training in logic to answer these questions correctly. AR questions are intended to be answered using knowledge, skills, and reasoning ability generally expected of college students and graduates.

Explore This Section

Suggested Approach for Analytical Reasoning
Analytical Reasoning Sample Questions

IMAGES

15 Deductive Reasoning Examples (2024)
Deductive Reasoning: Definition and Examples
What Is Deductive Reasoning
Problem Solving Deductive Reasoning Math Examples
What Is Deductive Reasoning? Definition, Examples & How To Use It
Deductive Reasoning: Examples, Definition, Types and the difference

VIDEO

Introduction to Problem Solving Inductive and Deductive Reasoning
Foundations of Reasoning
||REASONING PRACTICE SET 12|UPP
Mathematics in the Modern World
Natural deduction problem 05
Deductive Reasoning, Problem solving patterns, Polya's Strategy II Mathematics in the Modern World

COMMENTS

15 Deductive Reasoning Examples (2024)
Deductive Logic. Inductive Logic. a) All bachelors have never married. ( General statement) a) It was sunny on the 1st of July last year. ( Specific statement) b) John is a man who has never been married. b) It was sunny on the 1st of July the year before last. c) Therefore, John is a bachelor.
What is Deductive Reasoning: Detailed Guide with Examples
Examples of Deductive Reasoning. Mark needs to calculate the area of a circle with a radius of 3 cm. He uses the formula A = π r ^ 2, leading to A = π × 9. From the initial premise of knowing the formula for the area of a circle, Mark deduces the area of this specific circle. Emily observes that all mammals have vertebrae.
What Is Deductive Reasoning?
Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It's often contrasted with inductive reasoning, where you start with specific observations and form general conclusions. Deductive reasoning is also called deductive logic or top-down reasoning. Note. Deductive reasoning is often confused ...
Deductive Reasoning (Definition + Examples)
Example 3: Deductive Reasoning in Math. Deductive reasoning is introduced in math classes to help students understand equations and create proofs. When math teachers discuss deductive reasoning, they usually talk about syllogisms. Syllogisms are a form of deductive reasoning that helps people discover the truth.
Deductive reasoning (video)
And go all the way down here and then check his answers, and eventually come up with the notion that if this is true, then this must also be true. So that is deductive reasoning. You start with facts, use logical steps or operations, or logical reasoning to come up with other facts. He's not estimating.
Logical Puzzles
A logical puzzle is a problem that can be solved through deductive reasoning. This page gives a summary of the types of logical puzzles one might come across and the problem-solving techniques used to solve them. One of the simplest types of logical puzzles is a syllogism. In this type of puzzle, you are given a set of statements, and you are required to determine some truth from those statements.
Deductive Reasoning: Explanation and Examples
I. Definition Deductive reasoning, or deduction, is one of the two basic types of logical inference. A logical inference is a connection from a first statement (a "premise") to a second statement ("the conclusion") for which the rules of logic show that if the first statement is true, the second statement should be true. Specifically, deductions are inferences which must be true—at ...
Deductive Reasoning
Deductive Reasoning Example in Math: The Pythagorean Theorem: if a triangle has sides of lengths a, b, and c, where c is the hypotenuse (the longest side), then a² + b² = c². When to use Deductive Reasoning. Problem-Solving: Deductive reasoning can be used to solve problems in everyday life, ...
Inductive & deductive reasoning (video)
Inductive reasoning is when you start with true statements about specific things and then make a more general conclusion. For example: "All lifeforms that we know of depend on water to exist. Therefore, any new lifeform we discover will probably also depend on water." A conclusion drawn from inductive reasoning always has the possibility of ...
Intro to Deductive Reasoning: Definition and Examples
How to Include Deductive Reasoning Skills in a Job Application. The best way to show your deductive reasoning skills to a potential employer is to walk through your decision-making process while solving a problem. Even if you don't have professional work experience, refer to when you had to test a hypothesis and use your logical thinking ...
3.4: Inductive and Deductive Reasoning
Habanero sauce makes me teary. This is an example of deductive reasoning because the premises are general statements, while the conclusion is specific. 3.4: Inductive and Deductive Reasoning is shared under a license and was authored, remixed, and/or curated by LibreTexts. A logical argument is a claim that a set of premises support a conclusion.
Deductive Reasoning: What It Is, Uses & Examples
Deductive reasoning is a psychological process that people use to make decisions and solve problems. It's a cognitive function, meaning it's a conscious intellectual activity like thinking and understanding. In deductive reasoning, you use general ideas or premises to come to a specific conclusion. If you're like most people, you use ...
PDF Chapter 1: Problem Solving: Strategies and Principles
Problem Solving. We want to divide a circle into regions by selecting points on its circumference and drawing line segments from each point to each other point. The figure (on the next slide) shows the greatest number of regions that we get if we have one point (no line segment is possible for this case), two, three, and four points.
Deductive Reasoning: Definition, Types and Examples
You can apply the deductive reasoning process to your problem-solving efforts by first identifying an accurate assumption you can use as a foundation for your solution. Deductive reasoning often leads to fewer errors because it reduces the guesswork. Teamwork Many organizations expect employees to work together in teams to achieve results ...
DEDUCTIVE REASONING
Deductive reasoning uses general procedures and principles to reach a conclusion.Learn about the process of solving different deductive reasoning problems in...
Deductive Reasoning Examples
Deductive reasoning is a process of drawing conclusions. These deductive reasoning examples in science and life show when it's right - and when it's wrong.
Deductive Reasoning: What It Is, Why It's Important, and Examples
Deductive reasoning, also referred to as deductive logic or top-down thinking, is a type of logical thinking that's used in various industries and is often sought after by employers in new talent. The following is a formula often used in deduction: If A = B and B = C, then in most cases A = C. So, for example, if traffic gets bad starting at ...
PROBLEM SOLVING: INDUCTIVE AND DEDUCTIVE REASONING
In this video you will learn to define the terms and concepts problem solving and employ inductive and deductive reasoning in problem solving. References: Au...
How to Improve Your Deductive Reasoning Skills (With Examples ...
Problem-solving Employees can use deductive reasoning to come up with logical solutions to problems that are impacting an organization. To do this, you will first need to ask questions to form the premise of your argument, the statement that you are holding as truth. Example: You realized your furniture company is spending a lot of money each ...
What is Deductive Reasoning? Definition and Examples
Syllogism. Syllogism is probably the most simple of the 3 types of deductive reasoning. In simplest terms syllogism states that if A=B and B=C, then A=C. It takes two separate clauses and connects them together. A more creative example would be: a puma is a cat, cats are mammals, therefore pumas are mammals. Modus Ponens.
Inductive vs Deductive Reasoning
The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory. Inductive reasoning moves from specific observations to broad generalisations, and deductive reasoning the other way around. Both approaches are used in various types ...
Deductive reasoning test: Guidelines & Practice Examples
Deductive reasoning test measures a candidate's abilities to make logical deductions for problem-solving. Through the test, the candidates can usually demonstrate themselves to possess potential good qualities such as analytical thinking, good decision-making skill, and a problem-solving mindset.
Deductive Reasoning
Deductive reasoning plays an important role in various fields, heling in logical thinking, problem-solving, and decision-making processes. Here are some of the applications of Deductive Reasoning : Deductive reasoning helps break down complex problems into manageable parts and derive logical solutions.
PDF 1.1 Solving Problems by Inductive Reasoning
Deductive Reasoning Deductive reasoning is characterized by applying general principles to specific examples. The Moscow papyrus, which dates back to about 1850 B.C., provides an example of inductive reasoning by the early Egyptian mathematicians. Problem 14 in the document reads: You are given a truncated pyramid of 6 for the vertical
Analytical Reasoning
AR questions test a range of deductive reasoning skills: Comprehending the basic structure of a set of relationships by determining a complete solution to the problem posed (for example, an acceptable seating arrangement of all six diplomats around a table) Reasoning with conditional ("if-then") statements
Boost Problem-Solving with Logical Reasoning in Communication
Recognizing logical fallacies—errors in reasoning that undermine the logic of an argument—is crucial for effective problem-solving in communication. Fallacies can mislead your audience and ...
Enhancing Real-World Problem-Solving Skills in Mathematics
1-2 Inductive and Deductive Reasoning Overview: Inductive vs. Deductive Reasoning Have you ever played games such as Sudoku or solved logic puzzles? If so, you have practiced inductive and deductive reasoning skills. Inductive reasoning is the process of developing a general conclusion based on observations in given specific examples.
Articles about Reasoning
This classic example of deductive reasoning begins with a broad principle and then applies that principle to a particular person. The premises lead inevitably to the conclusion, which makes a more specific claim than the premises. ... Analogy-based reasoning plays an important role in problem-solving, decision-making, and creative thinking. Try ...

15 Deductive Reasoning Examples

Deductive Reasoning Examples

The Examples Explained

2. Buying Second-Hand Clothes

4. Socrates is Mortal

5. Zodiac Signs

6. Applying to Law School

7. Driver’s License

8. Public School Age Requirement

9. Protected Wildlife and Endangered Species

10. Fruits and Seeds

11. Baking a Cake

12. Change of Seasons

13. Competing in a Triathlon

14. Graduating with a Philosophy Degree

15. Paying Rent

2 thoughts on “15 Deductive Reasoning Examples”

Leave a Comment Cancel Reply

Definition of Deductive Reasoning

Modus Ponens

Modus Tollens

Related Posts

What Is Standard Form in Math: Step-by-Step Guide

Removable Discontinuity: In-Depth Guides with Examples

Graphs of Common Functions: Linear, Quadratic, Exponential & More

Deductive Reasoning (Definition + Examples)

Top-Down vs. Bottom-Up Logic

Understanding Correlation in Reasoning

What is Deductive Reasoning?

Characteristics of deductive reasoning

False Premises

Lack of Entailment

Narrow Truth

Example 1: All humans are mortal. Susan is a human. Susan is mortal.

Example 2: Marketing

Example 3: Deductive Reasoning in Math

Example 4: Deductive Reasoning in Science

Deductive vs inductive reasoning

Related posts:

About The Author

Psychology Resources

Psychology Tests

Logical Puzzles

Elimination Grids

This is the seventeenth problem of the set Winning Strategies.

Deductive Reasoning

II. Deductive Reasoning vs. Inductive Reasoning

Examples of inductive reasoning:

III. Quotations about Deductive reasoning

IV. The History and Importance of Deductive Reasoning

V. Deductive reasoning in Popular Culture

Deductive Reasoning – Definition, Types and Examples

Deductive Reasoning

Steps in Deductive Reasoning

Types of Deductive Reasoning

Categorical Syllogism

Hypothetical Syllogism

Disjunctive Syllogism

Categorical Logic

Applications of Deductive Reasoning

Deductive Reasoning Examples

When to use Deductive Reasoning

How to conduct Deductive Reasoning

Purpose of Deductive Reasoning

Advantages of Deductive Reasoning

Limitations of Deductive Reasoning

About the author

Muhammad Hassan

You may also like

Research Approach – Types Methods and Examples

Abductive Reasoning – Definition, Types and...

Inductive Reasoning – Definition, Types and Guide

Algebra (all content)

3.4: Inductive and Deductive Reasoning

Learning Objectives

Definition: Reasoning

Examples \(\PageIndex{1}\)

Definitions: Inductive and Deductive Reasoning

Examples \(\PageIndex{2}\)

What is Deductive Reasoning? Definition and Examples