Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.6 Negations of Conditional Statements and De Morgan's Law - Exercise Set 3.6 - Page 178: 47


See below.

Work Step by Step

The sentence in "if...then" form is: If there is no pain, there is no gain. The contrapositive of $p\rightarrow q$ is $\sim q\rightarrow \sim p$. The converse of $p\rightarrow q$ is $q \rightarrow p$. The inverse of $p\rightarrow q$ is $\sim p\rightarrow \sim q$. The negation of $ p\rightarrow q$ is $p\land \sim q$. Hence here the converse is: If there is no gain, then there is no pain. The inverse: If there is pain, then there is gain. The contrapositive: If there is gain, then there is pain. The negation: There is no pain and there is gain.
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