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: 45


The statements (a) and (b) are equivalents.

Work Step by Step

By using the following representation, \[\begin{align} & p:\text{ Im leaving} \\ & q:\text{ Tom is relieved} \\ & r:\text{ Sue is relieved} \end{align}\] The symbolic representation of the provided statements is (a)I’m leaving, and Tom is relieved or Sue is relieved: \[p\wedge \left( q\vee r \right)\]. (b)I’m leaving, and it is false that Tom and Sue are not relieved: \[p\wedge \sim \left( \sim q\wedge \sim r \right)\]. (c)If I’m leaving, then Tom is relieved or Sue is relieved: \[p\to \left( q\vee r \right)\].
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