# 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 “” 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?

• AFalse
• BTrue

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

• ATrue
• BFalse

Q2:

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

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 “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 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.

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