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: 23

Answer

a. Given any real number, you can find a real number so that the product of the two is 1. In other words, every real number has a multiplicative inverse. This statement is true. b. There is a real number with the following property: No matter what real number is multiplied to it, the product of the two will be 1. In other words, there is one particular real number whose product with any real number is 1. This statement is false; no one number will work for all numbers. For instance, if $x \cdot 1 = 1$, then x = 1, but in that case $x \cdot 2 = 2 \neq 1$.

Work Step by Step

Recall $\forall$ stands for "for all" and $\exists$ stands for "there exists."
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