# 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 ββ and be the conclusion β is prime.β

The conditional statement reads, βIf , then is prime.β Is this true or false?

• AFalse
• BTrue

The converse statement reads, βIf is prime, then .β Is this true or false?

• ATrue
• BFalse

The inverse statement reads, βIf , then is not prime.β Is this true or false?

• AFalse
• BTrue

The contrapositive statement reads, βIf is not prime, then .β Is this true or false?

• ATrue
• BFalse

Q2:

Consider the conditional statement βIf , 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 βIf 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.