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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.

Q1:

Let π΄ be the hypothesis β π₯ + 3 = 3 + π₯ β and π΅ be the conclusion β π₯ is prime.β

The conditional statement π΄ β π΅ reads, βIf π₯ + 3 = 3 + π₯ , then π₯ is prime.β Is this true or false?

The converse statement π΅ β π΄ reads, βIf π₯ is prime, then π₯ + 3 = 3 + π₯ .β Is this true or false?

The inverse statement Β¬ π΄ β Β¬ π΅ reads, βIf π₯ + 3 β 3 + π₯ , then π₯ is not prime.β Is this true or false?

The contrapositive statement Β¬ π΅ β Β¬ π΄ reads, βIf π₯ is not prime, then π₯ + 3 β 3 + π₯ .β Is this true or false?

Q2:

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

Q3:

Consider the conditional statement βIf π΄ , then π΅ ,β where the hypothesis π΄ is β π₯ and π¦ are even numbersβ and the conclusion π΅ is β π₯ + π¦ is even.β

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

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