Discrete Mathematics with Applications 4th Edition

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

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.1 - Page 106: 3

Answer

a. P(2): 2 > 1/2 is true P(1/2): 1/2 > $\frac{1}{1/2}$ = 2 is false P(-1): -1 > 1/-1 is false P(-1/2): -1/2 > -2 is true P(-8): -8 > -1/8 is false b. If the domain of P(x) is the set of all real numbers, then its truth set is the set of all real numbers x for which either x > 1 or −1 < x < 0. c. If the domain of P(x) is the set of all positive real numbers, then its truth set is the set of all real numbers x for which x > 1.

Work Step by Step

The truth set of P(x) is the set of all numbers in the domain of P(x) for which P(x) is true.
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