Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.4 - Predicates and Quantifiers - Exercises - Page 55: 36

Answer

a) For x=1, we have $x^{2}=1=x$ and thus x=1 is a counterexample. b) For $x= \sqrt 2$, we have $\sqrt 2^{2}=2$ and thus is $x=\sqrt 2$ a counterexample c) For x=0, we have $|x|=|0|=0$ which is not greater than zero, and thus x=0 is a counterexample.

Work Step by Step

a) For x=1, we have $x^{2}=1=x$ and thus x=1 is a counterexample. b) For $x= \sqrt 2$, we have $\sqrt 2^{2}=2$ and thus is $x=\sqrt 2$ a counterexample c) For x=0, we have $|x|=|0|=0$ which is not greater than zero, and thus x=0 is a counterexample.
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