# Worksheet: Analyzing Conditional Statements

In this worksheet, we will practice analyzing a given statement to identify hypothesis and conclusion to write it in if-then form; writing its converse, inverse, and contrapositive; constructing the conditional truth table; representing it using a Venn diagram; or identifying negations, conjunctions, and disjunctions.

Q1:

Read the following conditional statement: If it is raining, then Amelia has her umbrella up.

Write the converse of the statement.

• AIf it is not raining, then Amelia does not have her umbrella up.
• BIf Amelia does not have her umbrella up, then it is raining.
• CIf Amelia does not have her umbrella up, then it is not raining.
• DIf Amelia has her umbrella up, then it is raining.

Write the inverse of the statement.

• AIf it is not raining, then Amelia has her umbrella up.
• BIf it is not raining, then Amelia does not have her umbrella up.
• CIf Amelia does not have her umbrella up, then it is raining.
• DIf Amelia has her umbrella up, then it is raining.

Write the contrapositive of the statement.

• AIf Amelia does not have her umbrella up, then it is raining.
• BIf it is not raining, then Amelia does not have her umbrella up.
• CIf Amelia has her umbrella up, then it is raining.
• DIf Amelia does not have her umbrella up, then it is not raining.

Q2:

Read the following conditional statement: If Matthew does his homework, then he gets his weekly allowance.

What is the hypothesis?

• AMatthew does his homework.
• BMatthew gets his weekly allowance.

What is the conclusion?

• AHe does his homework.
• BHe gets his weekly allowance.

Q3:

Which of the following statements is true about the two planes? • AThe two planes are intersected.
• BThe two planes are parallel.
• CThe two planes are coincident.

Q4:

Complete using one of the choices below: If two planes have two common points and , then they .

• Aintersect at a straight line parallel to
• Bintersect at
• Chave a third point in common, which does not belong to
• Dare coincident

Q5:

Determine whether the following sentence is true or false: If is a quadrilateral, then there is only one plane passing through all of its sides.

• Afalse
• Btrue

Q6:

What does it mean for two lines to be considered skew?

• AThey are not parallel.
• BThey are located in the same plane.
• CThey are not coincident.
• DThey are not located in the same plane.

Q7:

Let be the hypothesis “” and be the conclusion “ is prime.”

The conditional statement reads, “If , then is prime.” Is this true or false?

• AFalse
• BTrue

The converse statement reads, “If is prime, then .” Is this true or false?

• ATrue
• BFalse

The inverse statement reads, “If , then is not prime.” Is this true or false?

• ATrue
• BFalse

The contrapositive statement reads, “If is not prime, then .” Is this true or false?

• ATrue
• BFalse

Q8:

Consider the conditional statement “If , then ,” where the hypothesis is “ and are even numbers” and the conclusion is “ is even.”

StatementIf , then .If , then .If not , then not .If not , then not .
True or False

Complete the table to give the truth value of the conditional statement and its converse, inverse, and contrapositive.

• ATrue, True, False, True
• BFalse, False, True, True
• CFalse, False, False, True
• DTrue, False, False, True
• ETrue, False, False, False

Q9:

Which of the following is the inverse of the conditional statement “If the measures of all the internal angles of a polygon are at most 180 degrees, then the polygon is convex?”

• AIf a polygon is convex, then the measures of all the internal angles are at most 180 degrees.
• BIf one of the internal angles of a polygon measures more than 180 degrees, then the polygon is not convex.
• CIf a polygon is not convex, then one of its internal angles measures more than 180 degrees.

Q10:

Decide whether the conclusion is valid.

Given: If two angles in a triangle add up to 70 degrees, then the triangle is obtuse.

Given: is an obtuse triangle.

Conclusion: Two of the angles in triangle add up to 70 degrees.

• AValid
• BNot valid

Q11:

William knows that the following statement is true: If it rains today, the grass will be wet.

The grass was wet on Monday. Can you conclude that it rained on Monday?

• AYes
• BNo

It rained on Tuesday. Can you conclude that the grass was wet on Tuesday?

• AYes
• BNo

Q12:

Which of the following statements follows logically from statements A and B?

1. If Liam misses the bus, then he will be late for work.
2. If Liam is late for work, then he will not be paid a bonus.
• AIf Liam was not paid a bonus, then he was late for work.
• BIf Liam misses the bus, then he will not be paid a bonus.
• CIf Liam is late for work, then he missed the bus.
• DIf Liam was not paid a bonus, then he missed the bus.

Q13:

Hannah knows that the following two statements are true:

• If a student does not complete their homework, they will get detention.
• If a student gets detention, they will be late home.

Jacob got detention and was late home.

Can we conclude that he did not complete his homework?

• ANo
• BYes

Jennifer did not do her homework.

Can we conclude that she was late home?

• AYes
• BNo

Q14:

We can use Venn diagrams to model conditional statements.

Which Venn diagram models the following two statements?

1. If an animal is a fish, then it lives in water.
2. Dolphins live in water.
• A • B • C • D Use the Venn diagram to determine whether the following statement is valid:

All dolphins are fish.

• ANot valid
• BValid

Q15:

Consider the following Venn diagram. Which conditional statement is represented by the diagram?

• AIf a student got an A, then they scored over .
• BIf a student scored over , then they got an A.

Use the Venn diagram to decide whether the following statement is valid: If Benjamin scored less than , then he did not get an A.

• ANot valid
• BValid