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: 32

Answer

See below.

Work Step by Step

The sentence in "if...then" form is: If a person is a senator, then he or she is a politician. 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 is a politician, then he or she is a senator. The inverse: If a person is not a senator, then he or she is not a politician. The contrapositive: If a person is not a politician, then he or she is not a senator.
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