Chapter 1, Problem 1GA

To determine

Whether the following statement is True/False.

“ $ab>0$ ” if $a>0$ and $b<0$

Answer to Problem 1GA

Solution:

The statement “ $ab>0$ ” is False if $a>0$ and $b<0$

Explanation of Solution

Multiplication of positive integer with negative integers always gives a negative integer.

Example: $3\times \left(-2\right)=-6$

Given:

$a>0$ and $b<0$

Calculation:

Given that $a>0$ and $b<0$

This implies that a is a positive integer and b is a negative integer.

Thus, $ab$ is a negative integer since multiplication of positive integer with negative integers always gives a negative integer.

Hence $ab<0$

Conclusion:

The statement “ $a>0$ ” is False if $a>0$ and $b<0$