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

Answer

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: \[p\to \left( q\vee r \right)\].
Small 1566404159
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.