Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 3 - Logic - 3.5 Equivalent Statements and Variations of Conditional Statements - Exercise Set 3.5 - Page 170: 21

See below.

Work Step by Step

The contrapositive of $p\rightarrow q$ is $\sim q\rightarrow p$. The converse of $p\rightarrow q$ is $q \rightarrow p$. The inverse of $p\rightarrow q$ is $\sim p\rightarrow q$. Hence here the converse is: If I cannot hear you, then the stereo is playing. The inverse: If the stereo is not playing, then I can hear you. The contrapositive: If I can hear you, then the stereo is not playing.

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