Lesson: Determine Truth Values of Negations, Conjunctions, and Disjunctions

In this lesson, we will learn how to analyze given statements, such as negations, conjunctions, or disjunctions, to determine the truth-value of its parts.

Sample Question Videos

  • 04:23

Worksheet: 3 Questions • 1 Video

Q1:

Let 𝐴 be the hypothesis β€œ π‘₯ + 3 = 3 + π‘₯ ” and 𝐡 be the conclusion β€œ π‘₯ is prime.”

The conditional statement 𝐴 β‡’ 𝐡 reads, β€œIf π‘₯ + 3 = 3 + π‘₯ , then π‘₯ is prime.” Is this true or false?

The converse statement 𝐡 β‡’ 𝐴 reads, β€œIf π‘₯ is prime, then π‘₯ + 3 = 3 + π‘₯ .” Is this true or false?

The inverse statement Β¬ 𝐴 β‡’ Β¬ 𝐡 reads, β€œIf π‘₯ + 3 β‰  3 + π‘₯ , then π‘₯ is not prime.” Is this true or false?

The contrapositive statement Β¬ 𝐡 β‡’ Β¬ 𝐴 reads, β€œIf π‘₯ is not prime, then π‘₯ + 3 β‰  3 + π‘₯ .” Is this true or false?

Q2:

Consider the conditional statement β€œIf 𝐴 , then 𝐡 ,” where the hypothesis 𝐴 is β€œ π‘₯ and 𝑦 are even numbers” and the conclusion 𝐡 is β€œ π‘₯ + 𝑦 is even.”

Statement If 𝐴 , then 𝐡 . If 𝐡 , then 𝐴 . If not 𝐴 , then not 𝐡 . If not 𝐡 , then not 𝐴 .
True or False

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

Q3:

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

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