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: 9

Answer

The statement is false when $x=0.5$

Work Step by Step

Written in standard english, the logical statement $\forall x\in \mathbb{R},x>1/x$ means "for all numbers $x$ in the set of real numbers, $x$ is greater than $\frac{1}{x}$." Since 0.5 is less than $\frac{1}{0.5}$, which is equal to $2$, this statement is not always true.
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