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 3.3 - Page 130: 44


a. This statement is true. The unique real number with the given property is 1. Note that 1· y = y for all real numbers y, and if x is any real number such that for instance, x ·2 = 2, then dividing both sides by 2 gives x = 2/2 = 1. b. This statement is false. Let x = 1 or -1. Both values of x result in 1/x being an integer. Hence x is not unique. c. This statement is true. There exists a unique y=-x which makes x+y=0 true. This is the additive inverse of x.

Work Step by Step

Recall that $\exists$ stands for "there exists" and $\exists$! stands for "there exists a unique" meaning there is one and only one such value.
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