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: 10


The statement is false when $a=-1$.

Work Step by Step

Written in standard english, the logical statement $\forall a\in \mathbb{Z},\frac{a-1}{a}\text{ is not an integer}$ means "for all numbers $a$ in the set of integers, $\frac{a-1}{a}$ is not an integer." When we plug $-1$ in for $a$, we get $\frac{-1-1}{-1}=\frac{-2}{-2}=2$, which is an integer. Therefore, the statement is false when $a$ = $-1$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.