Chapter 3.3, Problem 45PPE

To determine

The given statement is always, sometimes or never true.

Answer to Problem 45PPE

The given statement is sometimes true

Explanation of Solution

Given information:

Given that, $x>3$ and $y<1$

Calculation:

It is to be checked whether, $xy>0$ is always, sometimes or never true. Let, $x=4$ and $y=\frac{1}{2}$ Then

  $xy>0$

  $4\left(\frac{1}{2}\right)>?0$

  $2>0$

Again let, $x=4$ and $y=-\frac{1}{2}$ Then

  $xy>0$

  $4\left(-\frac{1}{2}\right)>?0$

  $-2\nprec 0$

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

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