# Worksheet: Determine Truth Values of Negations, Conjunctions, and Disjunctions

In this worksheet, we will practice analyzing given statements, such as negations, conjunctions, or disjunctions, to determine the truth-value of its parts.

**Q1: **

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?

- AFalse
- BTrue

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

- ATrue
- BFalse

**Q2: **

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, False, False, False
- BTrue, True, False, True
- CFalse, False, False, True
- DTrue, False, False, True
- EFalse, False, True, True

**Q3: **

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 a polygon is not convex, then one of its internal angles measures more than 180 degrees.
- CIf one of the internal angles of a polygon measures more than 180 degrees, then the polygon is not convex.