Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.2 - Page 49: 20


a. P is a square and P is not a rectangle. b. Today is New Year's Eve and tomorrow is not January. c. The decimal expansion of r is terminating and r is not rational. d. n is prime and n is neither odd nor 2. e. x is nonnegative and x is neither positive nor zero. f. Tom is Ann's father and either Jim is not her uncle or Sue is not her aunt. g. n is divisible by 6 and n is either not divisible by 2 or n is not divisible by 3.

Work Step by Step

The negation of "if p then q" is logically equivalent to "p and not q:" ~(p $\rightarrow$ q) $\equiv$ p $\land$ ~q. For sentences involving AND or OR, recall De Morgan's Laws: The negation of AND: ~(p $\land$ q) $\equiv$ ~p$\lor$ ~q The negation of OR: ~(p $\lor$ q) $\equiv$ ~p$\land$ ~q
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