## Discrete Mathematics with Applications 4th Edition

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