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: 25

Answer

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 Hence here the converse is: If all troops were withdrawn, then the president is telling the truth. The inverse: If the president is not telling the truth, then some troops were not withdrawn. The contrapositive: If some troops were not withdrawn, then the president was not telling the truth.
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