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 179: 52


See below.

Work Step by Step

The negation of $ p\rightarrow q$ is $p\land \sim q$. De Morgan's Laws says that $\sim (p\land q)\equiv \sim p\lor \sim q$ and $\sim (p\lor q)\equiv \sim p\land \sim q$. Thus here the negation is: $p\land \sim(\sim r\lor s)\equiv p\land ( r \land \sim s)$
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