Chapter 11, Problem 1R

To determine

The explanation for the values of either $a$ or $b$ if $ab=0$.

Answer to Problem 1R

Solution:

If $ab=0$ then either $a=0\text{ or }b=0$.

Explanation of Solution

Given information:

The provided equation is $ab=0$.

Consider the equation, $ab=0$

The equation $ab=0$, represents that the product of $a$ and $b$ is $0$.

The product of any real numbers can only be zero if either one of the number is equal to $0$.

By the property of zero, if $a$ is any real number then $a\cdot 0=0$.

So, if either $a=0$ or $b=0$, the product of $ab$ will certainly be equal to $0$.

Therefore, for $ab=0$, the values are either $a=0\text{ or }b=0$.