Chapter 3.1, Problem 61PPE

To determine

To give a counter example for the statement “If $x>y$ , then $x^2>y^2$ .”

Answer to Problem 61PPE

  $x=2\&y=-2$

Explanation of Solution

Given:

If $x>y$ , then $x^2>y^2$ .

Calculation:

Let $x=2\&y=-2$

Then

  $\begin{array}{l}{x}^2=2^2=4\\ y^2={\left(-2\right)}^2=4\end{array}$

Clearly,

  $\begin{array}{l}x>y\left[\because 2>-2\right]\\ \text{But}\\ x^2\cancel{>}{y}^2\left[\because 4\cancel{>}4\right]\end{array}$