Chapter 3.3, Problem 48PPE

To determine

The given statement is always, sometimes or never true.

Answer to Problem 48PPE

The given statement is sometimes true.

Explanation of Solution

Given information:

Given that, $x\ge 0$ and $y>1.$

Calculation:

It is to be checked whether, $xy>0$ is always, sometimes or never true. Let, $x=4$ and $y=2$ Then

  $\begin{array}{cc}xy& >0\\ 4(2)& >?0\\ 8& >0\end{array}$

Again let, $x=4$ and $y=0$

Then

  $\begin{array}{l}xy>0\\ 4(0)>0\\ 0\cancel{>}0\end{array}$

Hence for this problem, $xy>0$ is sometimes true.