hypothesis conditional statement example

Conditional Statement – Definition, Truth Table, Examples, FAQs

What is a conditional statement, how to write a conditional statement, what is a biconditional statement, solved examples on conditional statements, practice problems on conditional statements, frequently asked questions about conditional statements.

A conditional statement is a statement that is written in the “If p, then q” format. Here, the statement p is called the hypothesis and q is called the conclusion. It is a fundamental concept in logic and mathematics. 

Conditional statement symbol :  p → q

A conditional statement consists of two parts.

• The “if” clause, which presents a condition or hypothesis.
• The “then” clause, which indicates the consequence or result that follows if the condition is true. 

Example : If you brush your teeth, then you won’t get cavities.

Hypothesis (Condition): If you brush your teeth

Conclusion (Consequence): then you won’t get cavities 

Conditional Statement: Definition

A conditional statement is characterized by the presence of “if” as an antecedent and “then” as a consequent. A conditional statement, also known as an “if-then” statement consists of two parts:

• The “if” clause (hypothesis): This part presents a condition, situation, or assertion. It is the initial condition that is being considered.
• The “then” clause (conclusion): This part indicates the consequence, result, or action that will occur if the condition presented in the “if” clause is true or satisfied. 

Related Worksheets

Representation of Conditional Statement

The conditional statement of the form ‘If p, then q” is represented as p → q. 

It is pronounced as “p implies q.”

Different ways to express a conditional statement are:

• p implies q
• p is sufficient for q
• q is necessary for p

Parts of a Conditional Statement

There are two parts of conditional statements, hypothesis and conclusion. The hypothesis or condition will begin with the “if” part, and the conclusion or action will begin with the “then” part. A conditional statement is also called “implication.”

Conditional Statements Examples:

Example 1: If it is Sunday, then you can go to play. 

Hypothesis: If it is Sunday

Conclusion: then you can go to play. 

Example 2: If you eat all vegetables, then you can have the dessert.

Condition: If you eat all vegetables

Conclusion: then you can have the dessert 

To form a conditional statement, follow these concise steps:

Step 1 : Identify the condition (antecedent or “if” part) and the consequence (consequent or “then” part) of the statement.

Step 2 : Use the “if… then…” structure to connect the condition and consequence.

Step 3 : Ensure the statement expresses a logical relationship where the condition leads to the consequence.

Example 1 : “If you study (condition), then you will pass the exam (consequence).” 

This conditional statement asserts that studying leads to passing the exam. If you study (condition is true), then you will pass the exam (consequence is also true).

Example 2 : If you arrange the numbers from smallest to largest, then you will have an ascending order.

Hypothesis: If you arrange the numbers from smallest to largest

Conclusion: then you will have an ascending order

Truth Table for Conditional Statement

The truth table for a conditional statement is a table used in logic to explore the relationship between the truth values of two statements. It lists all possible combinations of truth values for “p” and “q” and determines whether the conditional statement is true or false for each combination. 

The truth value of p → q is false only when p is true and q is False. 

If the condition is false, the consequence doesn’t affect the truth of the conditional; it’s always true.

In all the other cases, it is true.

The truth table is helpful in the analysis of possible combinations of truth values for hypothesis or condition and conclusion or action. It is useful to understand the presence of truth or false statements. 

Converse, Inverse, and Contrapositive

The converse, inverse, and contrapositive are three related conditional statements that are derived from an original conditional statement “p → q.” 

Consider a conditional statement: If I run, then I feel great.

• Converse: 

The converse of “p → q” is “q → p.” It reverses the order of the original statement. While the original statement says “if p, then q,” the converse says “if q, then p.” 

Converse: If I feel great, then I run.

• Inverse: 

The inverse of “p → q” is “~p → ~q,” where “” denotes negation (opposite). It negates both the antecedent (p) and the consequent (q). So, if the original statement says “if p, then q,” the inverse says “if not p, then not q.”

Inverse : If I don’t run, then I don’t feel great.

• Contrapositive: 

The contrapositive of “p → q” is “~q → ~p.” It reverses the order and also negates both the statements. So, if the original statement says “if p, then q,” the contrapositive says “if not q, then not p.”

Contrapositive: If I don’t feel great, then I don’t run.

A biconditional statement is a type of compound statement in logic that expresses a bidirectional or two-way relationship between two statements. It asserts that “p” is true if and only if “q” is true, and vice versa. In symbolic notation, a biconditional statement is represented as “p ⟺ q.”

In simpler terms, a biconditional statement means that the truth of “p” and “q” are interdependent. 

If “p” is true, then “q” must also be true, and if “q” is true, then “p” must be true. Conversely, if “p” is false, then “q” must be false, and if “q” is false, then “p” must be false. 

Biconditional statements are often used to express equality, equivalence, or conditions where two statements are mutually dependent for their truth values. 

Examples : 

• I will stop my bike if and only if the traffic light is red.  
• I will stay if and only if you play my favorite song.

Facts about Conditional Statements

• The negation of a conditional statement “p → q” is expressed as “p and not q.” It is denoted as “𝑝 ∧ ∼𝑞.” 
• The conditional statement is not logically equivalent to its converse and inverse.
• The conditional statement is logically equivalent to its contrapositive. 
• Thus, we can write p → q ∼q → ∼p

In this article, we learned about the fundamentals of conditional statements in mathematical logic, including their structure, parts, truth tables, conditional logic examples, and various related concepts. Understanding conditional statements is key to logical reasoning and problem-solving. Now, let’s solve a few examples and practice MCQs for better comprehension.

Example 1: Identify the hypothesis and conclusion. 

If you sing, then I will dance.

Solution : 

Given statement: If you sing, then I will dance.

Here, the antecedent or the hypothesis is “if you sing.”

The conclusion is “then I will dance.”

Example 2: State the converse of the statement: “If the switch is off, then the machine won’t work.” 

Here, p: The switch is off

q: The machine won’t work.

The conditional statement can be denoted as p → q.

Converse of p → q is written by reversing the order of p and q in the original statement.

Converse of  p → q is q → p.

Converse of  p → q: q → p: If the machine won’t work, then the switch is off.

Example 3: What is the truth value of the given conditional statement? 

If 2+2=5 , then pigs can fly.

Solution:  

q: Pigs can fly.

The statement p is false. Now regardless of the truth value of statement q, the overall statement will be true. 

F → F = T

Hence, the truth value of the statement is true. 

Conditional Statement - Definition, Truth Table, Examples, FAQs

Attend this quiz & Test your knowledge.

What is the antecedent in the given conditional statement? If it’s sunny, then I’ll go to the beach.

A conditional statement can be expressed as, what is the converse of “a → b”, when the antecedent is true and the consequent is false, the conditional statement is.

What is the meaning of conditional statements?

Conditional statements, also known as “if-then” statements, express a cause-and-effect or logical relationship between two propositions.

When does the truth value of a conditional statement is F?

A conditional statement is considered false when the antecedent is true and the consequent is false.

What is the contrapositive of a conditional statement?

The contrapositive reverses the order of the statements and also negates both the statements. It is equivalent in truth value to the original statement.

RELATED POSTS

• Ordering Decimals: Definition, Types, Examples
• Decimal to Octal: Steps, Methods, Conversion Table
• Lattice Multiplication – Definition, Method, Examples, Facts, FAQs
• X Intercept – Definition, Formula, Graph, Examples
• Lateral Face – Definition With Examples

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

• 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.

2.11: If Then Statements

• Last updated
• Save as PDF
• Page ID 2144

Hypothesis followed by a conclusion in a conditional statement.

Conditional Statements

A conditional statement (also called an if-then statement ) is a statement with a hypothesis followed by a conclusion . The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.

If-then statements might not always be written in the “if-then” form. Here are some examples of conditional statements:

• Statement 1: If you work overtime, then you’ll be paid time-and-a-half.
• Statement 2: I’ll wash the car if the weather is nice.
• Statement 3: If 2 divides evenly into \(x\), then \(x\) is an even number.
• Statement 4: I’ll be a millionaire when I win the lottery.
• Statement 5: All equiangular triangles are equilateral.

Statements 1 and 3 are written in the “if-then” form. The hypothesis of Statement 1 is “you work overtime.” The conclusion is “you’ll be paid time-and-a-half.” Statement 2 has the hypothesis after the conclusion. If the word “if” is in the middle of the statement, then the hypothesis is after it. The statement can be rewritten: If the weather is nice, then I will wash the car. Statement 4 uses the word “when” instead of “if” and is like Statement 2. It can be written: If I win the lottery, then I will be a millionaire. Statement 5 “if” and “then” are not there. It can be rewritten: If a triangle is equiangular, then it is equilateral.

What if you were given a statement like "All squares are rectangles"? How could you determine the hypothesis and conclusion of this statement?

Example \(\PageIndex{1}\)

Determine the hypothesis and conclusion: I'll bring an umbrella if it rains.

Hypothesis: "It rains." Conclusion: "I'll bring an umbrella."

Example \(\PageIndex{2}\)

Determine the hypothesis and conclusion: All right angles are \(90^{\circ}\).

Hypothesis: "An angle is right." Conclusion: "It is \(90^{\circ}\)."

Example \(\PageIndex{3}\)

Use the statement: I will graduate when I pass Calculus.

Rewrite in if-then form and determine the hypothesis and conclusion.

This statement can be rewritten as If I pass Calculus, then I will graduate. The hypothesis is “I pass Calculus,” and the conclusion is “I will graduate.”

Example \(\PageIndex{4}\)

Use the statement: All prime numbers are odd.

Rewrite in if-then form, determine the hypothesis and conclusion, and determine whether this is a true statement.

This statement can be rewritten as If a number is prime, then it is odd. The hypothesis is "a number is prime" and the conclusion is "it is odd". This is not a true statement (remember that not all conditional statements will be true!) since 2 is a prime number but it is not odd.

Example \(\PageIndex{5}\)

Determine the hypothesis and conclusion: Sarah will go to the store if Riley does the laundry.

The statement can be rewritten as "If Riley does the laundry then Sarah will go to the store." The hypothesis is "Riley does the laundry" and the conclusion is "Sarah will go to the store."

Determine the hypothesis and the conclusion for each statement.

• If 5 divides evenly into \(x\), then \(x\) ends in 0 or 5.
• If a triangle has three congruent sides, it is an equilateral triangle.
• Three points are coplanar if they all lie in the same plane.
• If \(x=3\), then \(x^2=9\).
• If you take yoga, then you are relaxed.
• All baseball players wear hats.
• I'll learn how to drive when I am 16 years old.
• If you do your homework, then you can watch TV.
• Alternate interior angles are congruent if lines are parallel.
• All kids like ice cream.

Additional Resources

Video: If-Then Statements Principles - Basic

Activities: If-Then Statements Discussion Questions

Study Aids: Conditional Statements Study Guide

Practice: If Then Statements

Real World: If Then Statements

Calcworkshop

Conditional Statement If Then's Defined in Geometry - 15+ Examples!

// Last Updated: January 21, 2020 - Watch Video //

In today’s geometry lesson , you’re going to learn all about conditional statements!

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

We’re going to walk through several examples to ensure you know what you’re doing.

In addition, this lesson will prepare you for deductive reasoning and two column proofs later on.

Here we go!

What are Conditional Statements?

To better understand deductive reasoning, we must first learn about conditional statements.

A conditional statement has two parts: hypothesis ( if ) and conclusion ( then ).

In fact, conditional statements are nothing more than “If-Then” statements!

Sometimes a picture helps form our hypothesis or conclusion. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.

But to verify statements are correct, we take a deeper look at our if-then statements. This is why we form the converse , inverse , and contrapositive of our conditional statements.

What is the Converse of a Statement?

Well, the converse is when we switch or interchange our hypothesis and conclusion.

Conditional Statement : “If today is Wednesday, then yesterday was Tuesday.”

Hypothesis : “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.”

So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.

Converse : “If yesterday was Tuesday, then today is Wednesday.”

What is the Inverse of a Statement?

Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement.

So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”.

Inverse : “If today is not Wednesday, then yesterday was not Tuesday.”

What is a Contrapositive?

And the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both.

Contrapositive : “If yesterday was not Tuesday, then today is not Wednesday”

What is a Biconditional Statement?

A statement written in “if and only if” form combines a reversible statement and its true converse. In other words the conditional statement and converse are both true.

Continuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”

Biconditional : “Today is Wednesday if and only if yesterday was Tuesday.”

Examples of Conditional Statements

In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. And here’s a big hint…

Whenever you see “con” that means you switch! It’s like being a con-artist!

Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.

After this lesson, we will be ready to tackle deductive reasoning head-on, and feel confident as we march onward toward learning two-column proofs!

Conditional Statements – Lesson & Examples (Video)

• Introduction to conditional statements
• 00:00:25 – What are conditional statements, converses, and biconditional statements? (Examples #1-2)
• 00:05:21 – Understanding venn diagrams (Examples #3-4)
• 00:11:07 – Supply the missing venn diagram and conditional statement for each question (Examples #5-8)
• Exclusive Content for Member’s Only
• 00:17:48 – Write the statement and converse then determine if they are reversible (Examples #9-12)
• 00:29:17 – Understanding the inverse, contrapositive, and symbol notation
• 00:35:33 – Write the statement, converse, inverse, contrapositive, and biconditional statements for each question (Examples #13-14)
• 00:45:40 – Using geometry postulates to verify statements (Example #15)
• 00:53:23 – What are perpendicular lines, perpendicular planes and the perpendicular bisector?
• 00:56:26 – Using the figure, determine if the statement is true or false (Example #16)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

Get access to all the courses and over 450 HD videos with your subscription

Monthly and Yearly Plans Available

Get My Subscription Now

Still wondering if CalcWorkshop is right for you? Take a Tour and find out how a membership can take the struggle out of learning math.

Conditional Statement

A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning. In layman words, when a scientific inquiry or statement is examined, the reasoning is not based on an individual's opinion. Derivations and proofs need a factual and scientific basis. 

Mathematical critical thinking and logical reasoning are important skills that are required to solve maths reasoning questions.

In this mini-lesson, we will explore the world of conditional statements. We will walk through the answers to the questions like what is meant by a conditional statement, what are the parts of a conditional statement, and how to create conditional statements along with solved examples and interactive questions.

Lesson Plan  

What is meant by a conditional statement.

A statement that is of the form "If p, then q" is a conditional statement. Here 'p' refers to 'hypothesis' and 'q' refers to 'conclusion'.

For example, "If Cliff is thirsty, then she drinks water."

This is a conditional statement. It is also called an implication.

'\(\rightarrow\)' is the symbol used to represent the relation between two statements. For example, A\(\rightarrow\)B. It is known as the logical connector. It can be read as A implies B. 

Here are two more conditional statement examples

Example 1: If a number is divisible by 4, then it is divisible by 2.

Example 2: If today is Monday, then yesterday was Sunday.

What Are the Parts of a Conditional Statement?

Hypothesis (if) and Conclusion (then) are the two main parts that form a conditional statement.

Let us consider the above-stated example to understand the parts of a conditional statement.

Conditional Statement : If today is Monday, then yesterday was Sunday.

Hypothesis : "If today is Monday."

Conclusion : "Then yesterday was Sunday."

On interchanging the form of statement the relationship gets changed.

To check whether the statement is true or false here, we have subsequent parts of a conditional statement. They are:

• Contrapositive

Biconditional Statement

Let us consider hypothesis as statement A and Conclusion as statement B.

Following are the observations made:

Converse of Statement

When hypothesis and conclusion are switched or interchanged, it is termed as converse statement . For example,

Conditional Statement : “If today is Monday, then yesterday was Sunday.”

Hypothesis : “If today is Monday”

Converse : “If yesterday was Sunday, then today is Monday.”

Here the conditional statement logic is, If B, then A (B → A)

Inverse of Statement

When both the hypothesis and conclusion of the conditional statement are negative, it is termed as an inverse of the statement. For example,

Conditional Statement: “If today is Monday, then yesterday was Sunday”.

Inverse : “If today is not Monday, then yesterday was not Sunday.”

Here the conditional statement logic is, If not A, then not B (~A → ~B)

Contrapositive Statement

When the hypothesis and conclusion are negative and simultaneously interchanged, then the statement is contrapositive. For example,

Contrapositive: “If yesterday was not Sunday, then today is not Monday”

Here the conditional statement logic is, if not B, then not A (~B → ~A)

The statement is a biconditional statement when a statement satisfies both the conditions as true, being conditional and converse at the same time. For example,

Biconditional : “Today is Monday if and only if yesterday was Sunday.”

Here the conditional statement logic is, A if and only if B (A ↔ B)

How to Create Conditional Statements?

Here, the point to be kept in mind is that the 'If' and 'then' part must be true.

If a number is a perfect square , then it is even.

• 'If' part is a number that is a perfect square.

Think of 4 which is a perfect square.

This has become true.

• The 'then' part is that the number should be even. 4 is even.

This has also become true. 

Thus, we have set up a conditional statement.

Let us hypothetically consider two statements, statement A and statement B. Observe the truth table for the statements:

According to the table, only if the hypothesis (A) is true and the conclusion (B) is false then, A → B will be false, or else A → B will be true for all other conditions.

• A sentence needs to be either true or false, but not both, to be considered as a mathematically accepted statement.
• Any sentence which is either imperative or interrogative or exclamatory cannot be considered a mathematically validated statement. 
• A sentence containing one or many variables is termed as an open statement. An open statement can become a statement if the variables present in the sentence are replaced by definite values.

Solved Examples

Let us have a look at a few solved examples on conditional statements.

Identify the types of conditional statements.

There are four types of conditional statements:

• If condition
• If-else condition
• Nested if-else
• If-else ladder.

Ray tells "If the perimeter of a rectangle is 14, then its area is 10."

Which of the following could be the counterexamples? Justify your decision.

a) A rectangle with sides measuring 2 and 5

b) A rectangle with sides measuring 10 and 1

c) A rectangle with sides measuring 1 and 5

d) A rectangle with sides measuring 4 and 3

a) Rectangle with sides 2 and 5: Perimeter = 14 and area = 10

Both 'if' and 'then' are true.

b) Rectangle with sides 10 and 1: Perimeter = 22 and area = 10

'If' is false and 'then' is true.

c) Rectangle with sides 1 and 5: Perimeter = 12 and area = 5

Both 'if' and 'then' are false.

d) Rectangle with sides 4 and 3: Perimeter = 14 and area = 12

'If' is true and 'then' is false.

Joe examined the set of numbers {16, 27, 24} to check if they are the multiples of 3. He claimed that they are divisible by 9. Do you agree or disagree? Justify your answer.

Conditional statement : If a number is a multiple of 3, then it is divisible by 9.

Let us find whether the conditions are true or false.

a) 16 is not a multiple of 3. Thus, the condition is false. 

16 is not divisible by 9. Thus, the conclusion is false. 

b) 27 is a multiple of 3. Thus, the condition is true.

27 is divisible by 9. Thus, the conclusion is true. 

c) 24 is a multiple of 3. Thus the condition is true.

24 is not divisible by 9. Thus the conclusion is false.

Write the converse, inverse, and contrapositive statement for the following conditional statement. 

If you study well, then you will pass the exam.

The given statement is - If you study well, then you will pass the exam.

It is of the form, "If p, then q"

The converse statement is, "You will pass the exam if you study well" (if q, then p).

The inverse statement is, "If you do not study well then you will not pass the exam" (if not p, then not q).

The contrapositive statement is, "If you did not pass the exam, then you did not study well" (if not q, then not p).

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

Let's Summarize

The mini-lesson targeted the fascinating concept of the conditional statement. The math journey around conditional statements started with what a student already knew and went on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever.

About Cuemath

At  Cuemath , our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

FAQs on Conditional Statement

1. what is the most common conditional statement.

'If and then' is the most commonly used conditional statement.

2. When do you use a conditional statement?

Conditional statements are used to justify the given condition or two statements as true or false.

3. What is if and if-else statement?

If is used when a specified condition is true. If-else is used when a particular specified condition is not satisfying and is false.

4. What is the symbol for a conditional statement?

'\(\rightarrow\)' is the symbol used to represent the relation between two statements. For example, A\(\rightarrow\)B. It is known as the logical connector. It can be read as A implies B.

5. What is the Contrapositive of a conditional statement?

If not B, then not A (~B → ~A)

6. What is a universal conditional statement?

Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also known as an " If-then" statement. If the hypothesis is true and the conclusion is false, then the conditional statement is false. Likewise, if the hypothesis is false the whole statement is false. Conditional statements are also termed as implications.

Conditional Statement: If today is Monday, then yesterday was Sunday

Hypothesis: "If today is Monday."

Conclusion: "Then yesterday was Sunday."

If A, then B (A → B)

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school

• + ACCUPLACER Mathematics
• + ACT Mathematics
• + AFOQT Mathematics
• + ALEKS Tests
• + ASVAB Mathematics
• + ATI TEAS Math Tests
• + Common Core Math
• + DAT Math Tests
• + FSA Tests
• + FTCE Math
• + GED Mathematics
• + Georgia Milestones Assessment
• + GRE Quantitative Reasoning
• + HiSET Math Exam
• + HSPT Math
• + ISEE Mathematics
• + PARCC Tests
• + Praxis Math
• + PSAT Math Tests
• + PSSA Tests
• + SAT Math Tests
• + SBAC Tests
• + SIFT Math
• + SSAT Math Tests
• + STAAR Tests
• + TABE Tests
• + TASC Math
• + TSI Mathematics
• + ACT Math Worksheets
• + Accuplacer Math Worksheets
• + AFOQT Math Worksheets
• + ALEKS Math Worksheets
• + ASVAB Math Worksheets
• + ATI TEAS 6 Math Worksheets
• + FTCE General Math Worksheets
• + GED Math Worksheets
• + 3rd Grade Mathematics Worksheets
• + 4th Grade Mathematics Worksheets
• + 5th Grade Mathematics Worksheets
• + 6th Grade Math Worksheets
• + 7th Grade Mathematics Worksheets
• + 8th Grade Mathematics Worksheets
• + 9th Grade Math Worksheets
• + HiSET Math Worksheets
• + HSPT Math Worksheets
• + ISEE Middle-Level Math Worksheets
• + PERT Math Worksheets
• + Praxis Math Worksheets
• + PSAT Math Worksheets
• + SAT Math Worksheets
• + SIFT Math Worksheets
• + SSAT Middle Level Math Worksheets
• + 7th Grade STAAR Math Worksheets
• + 8th Grade STAAR Math Worksheets
• + THEA Math Worksheets
• + TABE Math Worksheets
• + TASC Math Worksheets
• + TSI Math Worksheets
• + AFOQT Math Course
• + ALEKS Math Course
• + ASVAB Math Course
• + ATI TEAS 6 Math Course
• + CHSPE Math Course
• + FTCE General Knowledge Course
• + GED Math Course
• + HiSET Math Course
• + HSPT Math Course
• + ISEE Upper Level Math Course
• + SHSAT Math Course
• + SSAT Upper-Level Math Course
• + PERT Math Course
• + Praxis Core Math Course
• + SIFT Math Course
• + 8th Grade STAAR Math Course
• + TABE Math Course
• + TASC Math Course
• + TSI Math Course
• + Number Properties Puzzles
• + Algebra Puzzles
• + Geometry Puzzles
• + Intelligent Math Puzzles
• + Ratio, Proportion & Percentages Puzzles
• + Other Math Puzzles

How to Understand ‘If-Then’ Conditional Statements: A Comprehensive Guide

In math, and even in everyday life, we often say 'if this, then that.' This is the essence of conditional statements. They set up a condition and then describe what happens if that condition is met. For instance, 'If it rains, then the ground gets wet.' These statements are foundational in math, helping us build logical arguments and solve problems. In this guide, we'll dive into the clear-cut world of conditional statements, breaking them down in both simple terms and their mathematical significance.

Step-by-step Guide: Conditional Statements

Defining Conditional Statements: A conditional statement is a logical statement that has two parts: a hypothesis (the ‘if’ part) and a conclusion (the ‘then’ part). Written symbolically, it takes the form: \( \text{If } p, \text{ then } q \) Where \( p \) is the hypothesis and \( q \) is the conclusion.

Truth Values: A conditional statement is either true or false. The only time a conditional statement is false is when the hypothesis is true, but the conclusion is false.

Converse, Inverse, and Contrapositive: 1. Converse: The converse of a conditional statement switches the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the converse is “If \( q \), then \( p \)”.

2. Inverse: The inverse of a conditional statement negates both the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the inverse is “If not \( p \), then not \( q \)”.

3. Contrapositive: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. For the statement “If \( p \), then \( q \)”, the contrapositive is “If not \( q \), then not \( p \)”.

Example 1: Simple Conditional Statement: “If it is raining, then the ground is wet.”

Solution: Hypothesis \(( p )\): It is raining. Conclusion \(( q )\): The ground is wet.

Example 2: Determining Truth Value Statement: “If a shape has four sides, then it is a rectangle.”

Solution: This statement is false because a shape with four sides could be a square, trapezoid, or other quadrilateral, not necessarily a rectangle.

Example 3: Converse, Inverse, and Contrapositive Statement: “If a number is even, then it is divisible by \(2\).”

Solution: Converse: If a number is divisible by \(2\), then it is even. Inverse: If a number is not even, then it is not divisible by \(2\). Contrapositive: If a number is not divisible by \(2\), then it is not even.

Practice Questions:

• Write the converse, inverse, and contrapositive for the statement: “If a bird is a penguin, then it cannot fly.”
• Determine the truth value of the statement: “If a shape has three sides, then it is a triangle.”
• For the statement “If an animal is a cat, then it is a mammal,” which of the following is its converse? a) If an animal is a mammal, then it is a cat. b) If an animal is not a cat, then it is not a mammal. c) If an animal is not a mammal, then it is not a cat.
• Converse: If a bird cannot fly, then it is a penguin. Inverse: If a bird is not a penguin, then it can fly. Contrapositive: If a bird can fly, then it is not a penguin.
• The statement is true. A shape with three sides is defined as a triangle.
• a) If an animal is a mammal, then it is a cat.

by: Effortless Math Team about 6 months ago (category: Articles )

Effortless Math Team

Related to this article, more math articles.

• 4th Grade GMAS Math Worksheets: FREE & Printable
• Embark on Your ParaPro Math Mastery: Introducing the “ParaPro Math for Beginners” Companion eBook
• Top 10 Praxis Core Math Practice Questions
• Product Predictions: How to Estimate Multiplication in Word Problems
• Top 10 3rd Grade ACT Aspire Math Practice Questions
• 10 Most Common ASTB Math Questions
• 10 Must-Have Math Teacher Supplies
• How to Solve Parallel Lines and Transversals Problems? (+FREE Worksheet!)
• Top Calculators for the GED 2023: Quick Review
• Solving the Unsolvable: How to Master Systems of Non-linear Equations with Elimination

What people say about "How to Understand ‘If-Then’ Conditional Statements: A Comprehensive Guide - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Algebra I Study Guide A Comprehensive Review and Step-By-Step Guide to Preparing for Algebra I

Oar math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the oar math, shsat math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the shsat math, psat math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the psat math, act math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the act math, accuplacer math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the accuplacer math, pre-algebra study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the pre-algebra, asvab math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the asvab math, afoqt math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the afoqt math, hiset math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the hiset math, dat quantitative reasoning study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the dat quantitative reasoning, tsi math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the tsi math, tabe 11 & 12 math study guide 2020 – 2021 for level d a comprehensive review and step-by-step guide to preparing for the tabe math, ftce math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the ftce general knowledge math, ged math study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the ged math.

• ATI TEAS 6 Math
• ISEE Upper Level Math
• SSAT Upper-Level Math
• Praxis Core Math
• 8th Grade STAAR Math

Limited time only!

Save Over 45 %

It was $89.99 now it is $49.99

Login and use all of our services.

Effortless Math services are waiting for you. login faster!

Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

• Math Worksheets
• Math Courses
• Math Topics
• Math Puzzles
• Math eBooks
• GED Math Books
• HiSET Math Books
• ACT Math Books
• ISEE Math Books
• ACCUPLACER Books
• Premium Membership
• Youtube Videos

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

• Bulk Orders
• Refund Policy

Introduction to Proofs: An Active Exploration of Mathematical Language

Jennifer Firkins Nordstrom

Search Results:

Section 2.3 conditional statements, activity 2.3.1 . which type., activity 2.3.2 . relationship between universal and conditional., example 2.3.1 . universal conditional statement..

Translate the statement using quantifiers and variables, “If an integer is even then it is divisible by 2.” Answer . Let \(P(x)\) be “ \(x\) is even” and \(Q(x)\) be “ \(x\) is divisible by 2.” \(\forall x\in \mathbb{Z}, P(x)\rightarrow Q(x)\text{.}\)

Activity 2.3.3 . Translating to Universal Conditional.

Activity 2.3.4 . a geography conditional., activity 2.3.5 . a weather conditional., activity 2.3.6 . an argument conditional., activity 2.3.7 . a mathematical conditional., logical equivalences for conditionals..

• \(\displaystyle p\rightarrow q\equiv \neg p\ \vee q\)
• \(\displaystyle \neg(p\rightarrow q)\equiv p\ \wedge \neg q\)

Definition 2.3.2 .

• contrapositive : \(\neg q\rightarrow \neg p\text{;}\)
• converse : \(q\rightarrow p\text{;}\)
• inverse : \(\neg p\rightarrow \neg q\text{.}\)

Definition 2.3.3 .

Definition 2.3.4 ., activity 2.3.8 . writing contrapositives., activity 2.3.9 . more writing contrapositives., activity 2.3.10 . converse statements., converting an argument to a conditional statement., example 2.3.5 . converting and argument to a conditional., example 2.3.6 . converting and argument to a conditional., activity 2.3.11 . checking validity with conditional., activity 2.3.12 . more checking validity with conditional., exercises exercises.

• Given any positive real number \(r\text{,}\) the reciprocal of ___.
• For any real number \(r\text{,}\) if \(r\) is ___ then ___.
• If a real number \(r\) ___, then ___.
• Given any negative real number \(s\text{,}\) the cube root of ___.
• For any real number \(s\text{,}\) if \(s\) is ___, then ___.
• If a real number \(s\) ___, then ___.
• There are real numbers \(u\) and \(v\) with the property that \(u+v < v-u\text{.}\)
• There is a real number \(x\) such that \(x^2 < x\text{.}\)
• For all positive integers \(n\text{,}\) \(n^2\geq n\text{.}\)
• For all real numbers \(a\) and \(b\text{,}\) \(| a+b | \leq | a | + | b |\text{.}\)
• All nonzero real numbers ___.
• For all nonzero real numbers \(r\text{,}\) there is ___ for \(r\text{.}\)
• For all nonzero real numbers \(r\text{,}\) there is a real number \(s\) such that ___.
• \(\forall\) real numbers \(x\text{,}\) if \(x>3\) then \(x^2>9\text{.}\)
• \(\forall n\in \mathbb{Z}\text{,}\) if \(n\) is prime then \(n\) is odd or \(n=2\text{.}\)
• \(\forall\) integers \(n\text{,}\) if \(n\) is divisible by 6, then \(n\) is divisible by 2 and \(n\) is divisible by 3.

Become a math whiz with AI Tutoring, Practice Questions & more.

Conditional Statements

Two common types of statements found in the study of logic are conditional and biconditional statements. They are formed by combining two statements which we then we call compound statements. What if we were to say, "If it snows, then we don't go outside." This is two statements combined. They are often called if-then statements. As in, "IF it snows, THEN we don't go outside." They are a fundamental building block of computer programming.

Writing conditional statements

A statement written in if-then format is a conditional statement.

It looks like

This represents the conditional statement:

"If p then q ."

A conditional statement is also called an implication.

If a closed shape has three sides, then it is a triangle.

The part of the statement that follows the "if" is called the hypothesis. The part of the statement that follows the "then" is the conclusion.

So in the above statement,

If a closed shape has three sides, (this is the hypothesis)

Then it is a triangle. (this is the conclusion)

Identify the hypothesis and conclusion of the following conditional statement.

A polygon is a hexagon if it has six sides.

Hypothesis: The polygon has six sides.

Conclusion: It is a hexagon.

The hypothesis does not always come first in a conditional statement. You must read it carefully to determine which part of the statement is the hypothesis and which part is the conclusion.

Truth table for conditional statement

The truth table for any two given inputs, say A and B , is given by:

• If A and B are both true, then A → B is true.
• If A is true and B is false, then A → B is false.
• If A is false and B is true, then A → B is true.
• If A and B are both false, then A → B is true.

Take our conditional statement that if it snows, we do not go outside.

If it is snowing ( A is true) and we do go outside ( B is false), then the statement A → B is false.

If it is not snowing ( A is false), it doesn't matter if we go outside or not ( B is true or false), because A → B is impossible to determine if A is false, so the statement A → B can still be true.

Biconditional statements

A biconditional statement is a combination of a statement and its opposite written in the format of "if and only if."

For example, "Two line segments are congruent if and only if they are the same length."

This is a combination of two conditional statements.

"Two line segments are congruent if they are the same length."

"Two line segments are the same length if they are congruent."

A biconditional statement is true if and only if both the conditional statements are true.

Biconditional statements are represented by the symbol:

p ↔ q

p ↔ q = p → q ∧ q → p

Writing biconditional statements

Write the two conditional statements that make up this biconditional statement:

I am punctual if and only if I am on time to school every day.

The two conditional statements that have to be true to make this statement true are:

• I am punctual if I am on time to school every day.
• I am on time to school every day if I am punctual.

A rectangle is a square if and only if the adjacent sides are congruent.

• If the adjacent sides of a rectangle are congruent then it is a square.
• If a rectangle is a square then the adjacent sides are congruent.

Topics related to the Conditional Statements

Conjunction

Counter Example

Biconditional Statement

Flashcards covering the Conditional Statements

Symbolic Logic Flashcards

Introduction to Proofs Flashcards

Practice tests covering the Conditional Statements

Introduction to Proofs Practice Tests

Get help learning about conditional statements

Understanding conditional statements can be tricky, especially when it gets deeper into programming language. If your student needs a boost in their comprehension of conditional statements, have them meet with an expert tutor who can give them 1-on-1 support in a setting free from distractions. A tutor can work at your student's pace so that tutoring is efficient while using their learning style - so that tutoring is effective. To learn more about how tutoring can help your student master conditional statements, contact the Educational Directors at Varsity Tutors today.

• ASCP Board of Certification - American Society for Clinical Pathology Board of Certification Training
• Holistic Medicine Tutors
• Internal Medicine Tutors
• DAT Courses & Classes
• Haitian Creole Tutors
• North Carolina Bar Exam Courses & Classes
• Actuarial Exam PA Test Prep
• Spanish 3 Tutors
• SSAT Test Prep
• Livonian Tutors
• Computer Programming Tutors
• CISM - Certified Information Security Manager Courses & Classes
• ARM - Associate in Risk Management Courses & Classes
• Arizona Bar Exam Test Prep
• SHSAT Test Prep
• REGENTS Tutors
• Series 57 Tutors
• WEST-E Test Prep
• Honors Science Tutors
• High School Level American Literature Tutors
• Kansas City Tutoring
• Austin Tutoring
• San Francisco-Bay Area Tutoring
• Buffalo Tutoring
• Philadelphia Tutoring
• Louisville Tutoring
• Atlanta Tutoring
• Dayton Tutoring
• San Antonio Tutoring
• Albuquerque Tutoring
• GRE Tutors in Los Angeles
• ACT Tutors in Philadelphia
• LSAT Tutors in Washington DC
• English Tutors in Atlanta
• SSAT Tutors in Los Angeles
• Physics Tutors in Seattle
• French Tutors in Seattle
• SSAT Tutors in Dallas Fort Worth
• ISEE Tutors in Dallas Fort Worth
• English Tutors in San Diego

Talk to our experts

1800-120-456-456

• Conditional Statement

What Is A Conditional Statement?

In mathematics, we define statement as a declarative statement which may either be true or may be false. Often sentences that are mathematical in nature may not be a statement because we might not know what the variable represents. For example, 2x + 2 = 5. Now here we do not know what x represents thus if we substitute the value of x (let us consider that x = 3) i.e., 2 × 3 = 6. Therefore, it is a false statement. So, what is a conditional statement? In simple words, when through a statement we put a condition on something in return of something, we call it a conditional statement. For example, Mohan tells his friend that “if you do my homework, then I will pay you 50 dollars”. So what is happening here? Mohan is paying his friend 50 dollars but places a condition that if only he’s work will be completed by his friend. A conditional statement is made up of two parts. First, there is a hypothesis that is placed after “if” and before the comma and second is a conclusion that is placed after “then”. Here, the hypothesis will be “you do my homework” and the conclusion will be “I will pay you 50 dollars”. Now, this statement can either be true or may be false. We don’t know. 

A hypothesis is a part that is used after the 'if' and before the comma. This composes the first part of a conditional statement. For example, the statement, 'I help you get an A+ in math,' is a hypothesis because this phrase is coming in between the 'if' and the comma. So, now I hope you can spot the hypothesis in other examples of a conditional statement. Of course, you can. Here is a statement: 'If Miley gets a car, then Allie's dog will be trained,' the hypothesis here is, 'Miley gets a car.' For the statement, 'If Tom eats chocolate ice cream, then Luke eats double chocolate ice cream,' the hypothesis here is, 'Tom eats chocolate ice cream. Now it is time for you to try and locate the hypothesis for the statement, 'If the square is a rectangle, then the rectangle is a quadrilateral'?

A conclusion is a part that is used after “then”. This composes the second part of a conditional statement. For example, for the statement, “I help you get an A+ in math”, the conclusion will be “you will give me 50 dollars”. The next statement was “If Miley gets a car, then Allie's dog will be trained”, the conclusion here is Allie's dog will be trained. It is the same with the next statement and for every other conditional statement.   

How Do We Know If A Statement Is True or False? 

In mathematics, the best way we can know if a statement is true or false is by writing a mathematical proof. Before writing a proof, the mathematician must find if the statement is true or false that can be done with the help of exploration and then by finding the counterexample. Once the proof is discovered, the mathematician must communicate this discovery to those who speak the language of maths. 

Converse, Inverse, contrapositive, And Bi-conditional Statement

We usually use the term “converse” as a verb for talking and chatting and as a noun we use it to represent a brand of footwear. But in mathematics, we use it differently. Converse and inverse are the two terms that are a connected concept in the making of a conditional statement.

If we want to create the converse of a conditional statement, we just have to switch the hypothesis and the conclusion. To create the inverse of a conditional statement, we have to turn both the hypothesis and the conclusion to the negative. A contrapositive statement can be made if we first interchange the hypothesis and conclusion then make them both negative. In a bi-conditional statement, we use “if and only if” which means that the hypothesis is true only if the condition is true. For example, 

If you eat junk food, then you will gain weight is a conditional statement.

If you gained weight, then you ate junk food is a converse of a conditional statement.

If you do not eat junk food, then you will not gain weight is an inverse of a conditional statement.

If yesterday was not Monday, then today is not Tuesday is a contrapositive statement. 

Today is Tuesday if and only if yesterday was Monday is a bi-conventional statement.   

Image will be uploaded soon

A Conditional Statement Truth Table

In the table above, p→q will be false only if the hypothesis(p) will be true and the conclusion(q) will be false, or else p→q will be true. 

Conditional Statement Examples

Below, you can see some of the conditional statement examples.

Example 1) Given, P = I do my work; Q = I get the allowance

What does p→q represent?

Solution 1) In the sentence above, the hypothesis is “I do my work” and the conclusion is “ I get the allowance”. Therefore, the condition p→q represents the conditional statement, “If I do my work, then I get the allowance”. 

Example 2) Given, a = The sun is a ball of gas; b = 5 is a prime number. Write a→b in a sentence. 

Solution 2) The conditional statement a→b here is “if the sun is a ball of gas, then 5 is a prime number”.

FAQs on Conditional Statement

1. How many types of conditional statements are there?

There are basically 5 types of conditional statements.

If statement, if-else statement, nested if-else statement, if-else-if ladder, and switch statement are the basic types of conditional statements. If a function displays a statement or performs a function on the condition if the statement is true. If-else statement executes a block of code if the condition is true but if the condition is false, a new block of code is placed. The switch statement is a selection control mechanism that allows the value of a variable to change the control flow of a program. 

2. How are a conditional statement and a loop different from each other?

A conditional statement is sometimes used by a loop but a loop is of no use to a conditional statement. A conditional statement is basically a “yes” or a “no” i.e., if yes, then take the first path else take the second one. A loop is more like a cyclic chain starting from the start point i.e., if yes, then take path a, if no, take path b and it comes back to the start point. 

Conditional statement executes a statement based on a condition without causing any repetition. 

A loop executes a statement repeatedly. There are two loop variables i.e., for loop and while loop.

• 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.

17.6: Truth Tables: Conditional, Biconditional

• Last updated
• Save as PDF
• Page ID 34287

• David Lippman
• Pierce College via The OpenTextBookStore

We discussed conditional statements earlier, in which we take an action based on the value of the condition. We are now going to look at another version of a conditional, sometimes called an implication, which states that the second part must logically follow from the first.

Conditional

A conditional is a logical compound statement in which a statement \(p\), called the antecedent, implies a statement \(q\), called the consequent.

A conditional is written as \(p \rightarrow q\) and is translated as "if \(p\), then \(q\)".

The English statement “If it is raining, then there are clouds is the sky” is a conditional statement. It makes sense because if the antecedent “it is raining” is true, then the consequent “there are clouds in the sky” must also be true.

Notice that the statement tells us nothing of what to expect if it is not raining; there might be clouds in the sky, or there might not. If the antecedent is false, then the consquent becomes irrelevant.

Suppose you order a team jersey online on Tuesday and want to receive it by Friday so you can wear it to Saturday’s game. The website says that if you pay for expedited shipping, you will receive the jersey by Friday. In what situation is the website telling a lie?

There are four possible outcomes:

1) You pay for expedited shipping and receive the jersey by Friday

2) You pay for expedited shipping and don’t receive the jersey by Friday

3) You don’t pay for expedited shipping and receive the jersey by Friday

4) You don’t pay for expedited shipping and don’t receive the jersey by Friday

Only one of these outcomes proves that the website was lying: the second outcome in which you pay for expedited shipping but don’t receive the jersey by Friday. The first outcome is exactly what was promised, so there’s no problem with that. The third outcome is not a lie because the website never said what would happen if you didn’t pay for expedited shipping; maybe the jersey would arrive by Friday whether you paid for expedited shipping or not. The fourth outcome is not a lie because, again, the website didn’t make any promises about when the jersey would arrive if you didn’t pay for expedited shipping.

It may seem strange that the third outcome in the previous example, in which the first part is false but the second part is true, is not a lie. Remember, though, that if the antecedent is false, we cannot make any judgment about the consequent. The website never said that paying for expedited shipping was the only way to receive the jersey by Friday.

A friend tells you “If you upload that picture to Facebook, you’ll lose your job.” Under what conditions can you say that your friend was wrong?

1) You upload the picture and lose your job

2) You upload the picture and don’t lose your job

3) You don’t upload the picture and lose your job

4) You don’t upload the picture and don’t lose your job

There is only one possible case in which you can say your friend was wrong: the second outcome in which you upload the picture but still keep your job. In the last two cases, your friend didn’t say anything about what would happen if you didn’t upload the picture, so you can’t say that their statement was wrong. Even if you didn’t upload the picture and lost your job anyway, your friend never said that you were guaranteed to keep your job if you didn’t upload the picture; you might lose your job for missing a shift or punching your boss instead.

In traditional logic, a conditional is considered true as long as there are no cases in which the antecedent is true and the consequent is false.

Truth table for the conditional

\(\begin{array}{|c|c|c|} \hline p & q & p \rightarrow q \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}\)

Again, if the antecedent \(p\) is false, we cannot prove that the statement is a lie, so the result of the third and fourth rows is true.

Construct a truth table for the statement \((m \wedge \sim p) \rightarrow r\)

We start by constructing a truth table with 8 rows to cover all possible scenarios. Next, we can focus on the antecedent, \(m \wedge \sim p\).

\(\begin{array}{|c|c|c|} \hline m & p & r \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \end{array}\)

\(\begin{array}{|c|c|c|c|} \hline m & p & r & \sim p \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}\)

\(\begin{array}{|c|c|c|c|c|} \hline m & p & r & \sim p & m \wedge \sim p \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \end{array}\)

Now we can create a column for the conditional. Because it can be confusing to keep track of all the Ts and \(\mathrm{Fs}\), why don't we copy the column for \(r\) to the right of the column for \(m \wedge \sim p\) ? This makes it a lot easier to read the conditional from left to right.

\(\begin{array}{|c|c|c|c|c|c|c|} \hline m & p & r & \sim p & m \wedge \sim p & r & (m \wedge \sim p) \rightarrow r \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}\)

When \(m\) is true, \(p\) is false, and \(r\) is false- -the fourth row of the table-then the antecedent \(m \wedge \sim p\) will be true but the consequent false, resulting in an invalid conditional; every other case gives a valid conditional.

If you want a real-life situation that could be modeled by \((m \wedge \sim p) \rightarrow r\), consider this: let \(m=\) we order meatballs, \(p=\) we order pasta, and \(r=\) Rob is happy. The statement \((m \wedge \sim p) \rightarrow r\) is "if we order meatballs and don't order pasta, then Rob is happy". If \(m\) is true (we order meatballs), \(p\) is false (we don't order pasta), and \(r\) is false (Rob is not happy), then the statement is false, because we satisfied the antecedent but Rob did not satisfy the consequent.

For any conditional, there are three related statements, the converse, the inverse, and the contrapositive.

Related Statments

The original conditional is \(\quad\) "if \(p,\) then \(q^{\prime \prime} \quad p \rightarrow q\)

The converse is \(\quad\) "if \(q,\) then \(p^{\prime \prime} \quad q \rightarrow p\)

The inverse is \(\quad\) "if not \(p,\) then not \(q^{\prime \prime} \quad \sim p \rightarrow \sim q\)

The contrapositive is "if not \(q,\) then not \(p^{\prime \prime} \quad \sim q \rightarrow \sim p\)

Consider again the conditional “If it is raining, then there are clouds in the sky.” It seems reasonable to assume that this is true.

The converse would be “If there are clouds in the sky, then it is raining.” This is not always true.

The inverse would be “If it is not raining, then there are not clouds in the sky.” Likewise, this is not always true.

The contrapositive would be “If there are not clouds in the sky, then it is not raining.” This statement is true, and is equivalent to the original conditional.

Looking at truth tables, we can see that the original conditional and the contrapositive are logically equivalent, and that the converse and inverse are logically equivalent.

Equivalence

A conditional statement and its contrapositive are logically equivalent.

The converse and inverse of a conditional statement are logically equivalent.

In other words, the original statement and the contrapositive must agree with each other; they must both be true, or they must both be false. Similarly, the converse and the inverse must agree with each other; they must both be true, or they must both be false.

Be aware that symbolic logic cannot represent the English language perfectly. For example, we may need to change the verb tense to show that one thing occurred before another.

Suppose this statement is true: “If I eat this giant cookie, then I will feel sick.” Which of the following statements must also be true?

• If I feel sick, then I ate that giant cookie.
• If I don’t eat this giant cookie, then I won’t feel sick.
• If I don’t feel sick, then I didn’t eat that giant cookie.
• This is the converse, which is not necessarily true. I could feel sick for some other reason, such as drinking sour milk.
• This is the inverse, which is not necessarily true. Again, I could feel sick for some other reason; avoiding the cookie doesn’t guarantee that I won’t feel sick.
• This is the contrapositive, which is true, but we have to think somewhat backwards to explain it. If I ate the cookie, I would feel sick, but since I don’t feel sick, I must not have eaten the cookie.

Notice again that the original statement and the contrapositive have the same truth value (both are true), and the converse and the inverse have the same truth value (both are false).

Try it Now 5

“If you microwave salmon in the staff kitchen, then I will be mad at you.” If this statement is true, which of the following statements must also be true?

• If you don’t microwave salmon in the staff kitchen, then I won’t be mad at you.
• If I am not mad at you, then you didn’t microwave salmon in the staff kitchen.
• If I am mad at you, then you microwaved salmon in the staff kitchen.

Choice b is correct because it is the contrapositive of the original statement.

Consider the statement “If you park here, then you will get a ticket.” What set of conditions would prove this statement false?

• You don’t park here and you get a ticket.
• You don’t park here and you don’t get a ticket.
• You park here and you don’t get a ticket.

The first two statements are irrelevant because we don’t know what will happen if you park somewhere else. The third statement, however contradicts the conditional statement “If you park here, then you will get a ticket” because you parked here but didn’t get a ticket. This example demonstrates a general rule; the negation of a conditional can be written as a conjunction: “It is not the case that if you park here, then you will get a ticket” is equivalent to “You park here and you do not get a ticket.”

The Negation of a Conditional

The negation of a conditional statement is logically equivalent to a conjunction of the antecedent and the negation of the consequent.

\(\sim(p \rightarrow q)\) is equivalent to \(p \wedge \sim q\)

Which of the following statements is equivalent to the negation of “If you don’t grease the pan, then the food will stick to it” ?

• I didn’t grease the pan and the food didn’t stick to it.
• I didn’t grease the pan and the food stuck to it.
• I greased the pan and the food didn’t stick to it.
• This is correct; it is the conjunction of the antecedent and the negation of the consequent. To disprove that not greasing the pan will cause the food to stick, I have to not grease the pan and have the food not stick.
• This is essentially the original statement with no negation; the “if…then” has been replaced by “and”.
• This essentially agrees with the original statement and cannot disprove it.

Try it Now 6

“If you go swimming less than an hour after eating lunch, then you will get cramps.” Which of the following statements is equivalent to the negation of this statement?

• I went swimming more than an hour after eating lunch and I got cramps.
• I went swimming less than an hour after eating lunch and I didn’t get cramps.
• I went swimming more than an hour after eating lunch and I didn’t get cramps.

Choice b is equivalent to the negation; it keeps the first part the same and negates the second part.

In everyday life, we often have a stronger meaning in mind when we use a conditional statement. Consider “If you submit your hours today, then you will be paid next Friday.” What the payroll rep really means is “If you submit your hours today, then you will be paid next Friday, and if you don’t submit your hours today, then you won’t be paid next Friday.” The conditional statement if t , then p also includes the inverse of the statement: if not t , then not p . A more compact way to express this statement is “You will be paid next Friday if and only if you submit your timesheet today.” A statement of this form is called a biconditional .

Biconditional

A biconditional is a logical conditional statement in which the antecedent and consequent are interchangeable.

A biconditional is written as \(p \leftrightarrow q\) and is translated as " \(p\) if and only if \(q^{\prime \prime}\).

Because a biconditional statement \(p \leftrightarrow q\) is equivalent to \((p \rightarrow q) \wedge(q \rightarrow p),\) we may think of it as a conditional statement combined with its converse: if \(p\), then \(q\) and if \(q\), then \(p\). The double-headed arrow shows that the conditional statement goes from left to right and from right to left. A biconditional is considered true as long as the antecedent and the consequent have the same truth value; that is, they are either both true or both false.

Truth table for the biconditional

\(\begin{array}{|c|c|c|} \hline p & q & p \leftrightarrow q \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}\)

Notice that the fourth row, where both components are false, is true; if you don’t submit your timesheet and you don’t get paid, the person from payroll told you the truth.

Suppose this statement is true: “The garbage truck comes down my street if and only if it is Thursday morning.” Which of the following statements could be true?

• It is noon on Thursday and the garbage truck did not come down my street this morning.
• It is Monday and the garbage truck is coming down my street.
• It is Wednesday at 11:59PM and the garbage truck did not come down my street today.
• This cannot be true. This is like the second row of the truth table; it is true that I just experienced Thursday morning, but it is false that the garbage truck came.
• This cannot be true. This is like the third row of the truth table; it is false that it is Thursday, but it is true that the garbage truck came.
• This could be true. This is like the fourth row of the truth table; it is false that it is Thursday, but it is also false that the garbage truck came, so everything worked out like it should.

Try it Now 7

Suppose this statement is true: “I wear my running shoes if and only if I am exercising.” Determine whether each of the following statements must be true or false.

• I am exercising and I am not wearing my running shoes.
• I am wearing my running shoes and I am not exercising.
• I am not exercising and I am not wearing my running shoes.

Choices a & b are false; c is true.

Create a truth table for the statement \((A \vee B) \leftrightarrow \sim C\)

Whenever we have three component statements, we start by listing all the possible truth value combinations for \(A, B,\) and \(C .\) After creating those three columns, we can create a fourth column for the antecedent, \(A \vee B\). Now we will temporarily ignore the column for \(C\) and focus on \(A\) and \(B\), writing the truth values for \(A \vee B\).

\(\begin{array}{|c|c|c|} \hline A & B & C \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \end{array}\)

\(\begin{array}{|c|c|c|c|} \hline A & B & C & A \vee B \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \end{array}\)

Next we can create a column for the negation of \(C\). (Ignore the \(A \vee B\) column and simply negate the values in the \(C\) column.)

\(\begin{array}{|c|c|c|c|c|} \hline A & B & C & A \vee B & \sim C \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}\)

Finally, we find the truth values of \((A \vee B) \leftrightarrow \sim C\). Remember, a biconditional is true when the truth value of the two parts match, but it is false when the truth values do not match.

\(\begin{array}{|c|c|c|c|c|c|} \hline A & B & C & A \vee B & \sim C & (A \vee B) \leftrightarrow \sim C \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \end{array}\)

To illustrate this situation, suppose your boss needs you to do either project \(A\) or project \(B\) (or both, if you have the time). If you do one of the projects, you will not get a crummy review ( \(C\) is for crummy). So \((A \vee B) \leftrightarrow \sim C\) means "You will not get a crummy review if and only if you do project \(A\) or project \(B\)." Looking at a few of the rows of the truth table, we can see how this works out. In the first row, \(A, B,\) and \(C\) are all true: you did both projects and got a crummy review, which is not what your boss told you would happen! That is why the final result of the first row is false. In the fourth row, \(A\) is true, \(B\) is false, and \(C\) is false: you did project \(A\) and did not get a crummy review. This is what your boss said would happen, so the final result of this row is true. And in the eighth row, \(A, B\), and \(C\) are all false: you didn't do either project and did not get a crummy review. This is not what your boss said would happen, so the final result of this row is false. (Even though you may be happy that your boss didn't follow through on the threat, the truth table shows that your boss lied about what would happen.)

• 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.

5.3.1: Conditional/Hypothetical Sentences

• Last updated
• Save as PDF
• Page ID 122497

• Don Bissonnette
• South Seattle Community College

Conditional/Hypothetical Sentences

       All conditional / hypothetical sentences consist of a dependent clause beginning with if (or other adverbials of condition) and an independent clause which is a result of the condition or hypothesis. A conditional sentence is one that is real or possibly can happen; a hypothetical sentence is one that is only imaginary - it either will not happen or did not happen.

Class One: Conditional

A.   Present or future situation: True and Real or Possible

If + present tense verb,     will or future implied verb ( c an, might, want, need, etc.)

          Examples:

If my sister visits Seattle, I will take her to Mount Rainier.

If we go there, I want to take a picnic lunch.

B.   General Truth situations, not for a specific time, something is always true and never changes.  It is True and Real or Possible

If + present tense verb,     present tense verb

         Examples:

If plants have good soil and get enough sunlight and water, they always grow well.

If a car runs out of gas, it stops.

C.  Past Situations: True and Completed Actions in the Past

Form:    

If + past tense,   past tense

If my father caught fish, he was happy.

If my grandmother cooked dinner when I was a boy, I always ate a lot.

D.  Alternate Form for the Present and Future Situations : Should

       We can use should in Class One conditional sentences in the present and future when we are not sure of the condition . Only if the condition happens will the result happen. It gives a feeling of uncertainty (not sure of something).

         Examples:

If you should receive a letter from John, please tell me. Should you receive a letter from John, please let me know.  

If you should get stopped by a policeman, you must have your driver's license with you or you will get a ticket.

Should you get stopped by a policeman, you must have your driver's license with you or you will get a ticket.

Class Two: Hypothetical

A.   Present or Future Situations - will not or are not very likely to occur- Not Real, Not Possible,                                                                                                            Only Imaginary

If + past tense verb,     would or could   + verb stem

          Examples:

If I had a million dollars, I would go on a long vacation.

If I played professional baseball, I could make a lot of money.

B.  Verb To Be: Were

In Class Two Conditionals, when you need to use the verb To Be , always use were after if . (This is called the subjunctive.)

If + subject + were ,     would or could + verb stem.

If I were a bird, I could fly.

If she were my daughter, I would love her.

C.  Alternate Form for Present Hypothetical Situations: Were    

      Were may be used in place of if to form the Class Two Conditionals; however, this is usually only done in very formal situations.

Were + noun,     would or could + verb stem

                                           or    

Were + subject + infinitive,     would or could + verb stem

Examples:    

If you were an American, you would not take ESL classes. Were you an American, you would not take ESL classes.

If I were a woman, I could have a baby. Were I a woman, I could have a baby.

If I bought a new car, my wife would be happy. Were I to buy a new car, my wife would be happy.

If I went to Russia, I would visit Moscow. Were I to go to Russia, I would visit Moscow.

Class Three: Hypothetical

    A.  Past Situations - Did Not Happen, Not Real, Imaginary

If + past perfect tense, past tense modal (would have, could have, might have, should have + past participle of verb)

 Examples:

If I had won the lottery last week, I would have bought a new car.

If you had grown up in America, you could have learned English as a child.

B.  Alternate Form with Had

The meaning is the same using this form; however, it has a more elegant sound to it.

Had + subject + past participle of verb, past tense modal.

If I had known your address, I would have visited you. Had I known your address, I would have visited you.

If you had stayed in your native country, you would not have had me as your teacher. Had you stayed in your native country, you would not have had me as your teacher.  

       Please note that with this alternate form that the negative is formed by making the past participle negative.

If I hadn't prepared this handout, this lesson would have been more difficult for you to understand.

Had I not prepared this handout, this lesson would have been more difficult to understand.

If I hadn't gone to Tunisia, I might not have learned to speak French. Had I not gone to Tunisia, I might not have learned to speak French.

If I hadn’t prepared this handout yesterday, we wouldn’t have studied it today.

Had I not prepared this handout yesterday, we wouldn’t have studied it today.

Class Four: Mixed Hypothetical - Past Influences the Present or Future

    Both situations are imaginary. Neither one is a fact.

    A past hypothetical situation (imaginary, did not happen, or is contrary to fact) influences a present or future hypothetical situation. This is actually a combination of a Class Three Conditional and a Class Two Conditional.

Form:      

If + past perfect tense,     would or could + verb stem.

    If my grandmother had taught me to speak Italian when I was a little boy, I would speak Italian as well as a native speaker of Italian now.  However, she didn’t teach me to speak Italian.

    If you had stayed in your native country, you could not attend this school.  However, you didn’t stay in your native country.  You came to America and to my class.  

Class Five: Mixed Hypothetical - Past Possible Influences the Present or Future

    The condition might have happened.  If it did, we know the results.

    A past situation - possibly real, possibly happened, but you do not know or are not sure - influences a real present or future situation.  This is actually a combination of a  Class One, Past Real Conditional, and a Class One, Present/Future Conditional.

If + past tense,     present tense or future tense.

If my sister won yesterday's lottery, she is definitely happy today.

If he fixed his car this morning, he will come to the party tonight.

We don’t know if the condition is real (or if it did happen), but we do know that if it is in fact true, then the result is for sure real.

Exercise 11:  Answer the following questions about hypothetical situations in the past that did not happen, please.

1.  What would you have done for a living if you had stayed in your native country?

2.  Would you have had me for a teacher if you had gone to a different college?

3.  What would you have done today if you had stayed home and not come to class?

4.  Would you have learned English if you had not come to America?

5.  What kind of restaurant would you have gone to last weekend if you had decided to eat out instead of eating in?

6.  How would your life have been different if you had learned English very well before you came to the United States?

7.  What kind of clothes would you have worn to school if it had snowed last night?

8.  What would you have done differently if you had been smarter as a younger person?

9.  If your teacher hadn’t come to class today, what would you have done?

10.  What would you have done if there had been a fire in your house last night?

11.  What might you have bought last week if you had had extra money?

12.  If you had already learned English perfectly before you came to America, what would you have studied at university?

13.  If you had won a million dollars in the lottery in your country, would you have come to America?

Exercise 12:  Complete the following past hypothetical (unreal) sentences, using the correct verb tenses, please.

1.  My father and mother would have graduated from university if

2.  If I had been in Japan during the earthquake and tsunami,

3.  If I had been born in America,

4.  I would have learned English as a child if

5.  I could have stayed in my native country if

6.  If my friend hadn’t smoked all her life,

7.  If there had been class on Friday afternoon,

8.  If I had studied harder as a young student,

9.  My friend’s wife might have learned how to swim if

10.  I could have gone to the party last weekend if

11.  If I had known that the restaurant was so expensive,

12.  If I had been arrested last night,

13.  If America hadn’t gotten into a war with Iraq,

14.  My son might have bought a car last weekend if

Exercise 13:  Complete these sentences, please.  Be careful to use the correct verb tenses.

1.  If it rains tomorrow,

2.  If I saw a tiger running loose in Seattle,

3.  If I had had more money,

4.  If my mother wants to make some tea,

5.  If I had ten children,

6.  If I had lived a thousand years ago,

7.  If people always did what they were supposed to do,

8.  If your teacher had gone to jail for twenty years,

9.  If it is sunny tomorrow,

10.  If my friend asked me to do him a favor,

11.  If my teacher hadn’t given me this homework assignment,

12.  If I weren’t an ESL student,

13.  If I graduate from college,

14.  If I had looked at this handout,

15.  If this were not the last sentence in this homework assignment,

Exercise 14:  Answer these questions, please.  Make sure to use the correct verb tenses.

1.  If you were a teacher, would you give a lot of homework to students?

2.  Should you run into me during the weekend, will you say hello?

3.  Were you to win the lottery, would you give some of the money away?

4.  Had you been President Bush, would you have gone to war with Iraq?

5.  If you get a high-paying job, will you buy a house?

6.  Had you stayed in your country, what would you be doing right now?

7.  If your mother cooked food for you as a child, did you eat it?

8.  Were your teacher to assign a composition for homework, would you do it?

9.  Had you been born the opposite sex, would your name still be the same as it is now?

10.  Might you have learned English had you stayed in your native country?

11.  Could you study English if you were an elephant?

12.  If you weighed as much as an elephant, could you buy your clothes in a regular store?

13.  Had you gone on a two-week vacation last Friday, would you be in class today?

14.  If I had married your mother, what would your relationship to me be?

15.  Were you ten years younger, where would you be right now?

Exercise 15:  Complete the following sentences, please.

1.  If I hadn’t completed my homework assignment before I came to class,

2.  My friend would come for a visit to Seattle if

3.  Some people steal

4.  Had I known a long time ago what I know now,

5.  I would love to spend a lot of time traveling around the world

6.  If I knew how to cook as well as my friend,

7.  Were I to become injured in an accident,

8.  If I lost my job,

9.  If I wake up early tomorrow morning,

10.  Should I get a ticket for speeding,

11.  Had I won last week’s lottery,

12.  If my parents were alive,

13.  I would have gone to the cinema on Saturday evening if

14.  Had I received a raise in pay last week,

15.  Were this not the last sentence in this exercise,