Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.1 - Page 161: 11


Let $a=-3$ and $b=0$. Then $a0^{2}=0$.

Work Step by Step

When looking for a counterexample to a mathematical statement, try searching systematically. In this case, it would be wise to try $a$ and $b$ both positive, $a$ and $b$ both negative, $a$ negative and $b$ positive, and so on. In this case, it turns out that $a\lt0$ and $b\geq$0 works whenever $|a|\gt|b|$.
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