Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.5 Equivalent Statements and Variations of Conditional Statements - Exercise Set 3.5 - Page 170: 31

Answer

See below.

Work Step by Step

The sentence in "if...then" form is: If a person diets, then he or she loses weight. 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 a person loses weight, then he or she is dieting. The inverse: If a person is not dieting, then he or she is not losing weight. The contrapositive: If a person is not losing weight, then he or she is not dieting.
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