# 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 ββ and be the conclusion β is prime.β

The conditional statement reads, βIf , then is prime.β Is this true or false?

- AFalse
- BTrue

The converse statement reads, βIf is prime, then .β Is this true or false?

- ATrue
- BFalse

The inverse statement reads, βIf , then is not prime.β Is this true or false?

- ATrue
- BFalse

The contrapositive statement reads, βIf is not prime, then .β Is this true or false?

- ATrue
- BFalse

**Q8: **

Consider the conditional statement βIf , then ,β where the hypothesis is β and are even numbersβ and the conclusion is β is even.β

Statement | If , 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 βIf the measures of all the internal angles of a polygon are at most 180 degrees, then the polygon is convex?β

- 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.

**Q12: **

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

- If Liam misses the bus, then he will be late for work.
- 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?

- If an animal is a fish, then it lives in water.
- 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