8. is the following statement true or false? justify your conclusion. if a and b are nonnegative real numbers and a + b =0, then a = 0. either give a counterexample to show that it is false or outline a proof by completing a know-show table.

If then and

a  | b | a + b (answer)

0 | 0 | 0

0 | 1  | 1

0 | 2 | 2

1  | 0 | 1

2 | 0 | 2

1  | 1  | 2

2 | 1  | 3

Step-by-step explanation:

Considering the following conditions for the real numbers:

Following the rules of these in-equations, it is possible to deduce:

Then, if the proposed statement is:

The conditions above shall comply the requirements established, but first, analyzing the statement:

If and then , and .

If and b a non negative real number, then , but because to , then . Due to the commutative property of sums, the same behavior will be presented if and a a non negative real number.

According to that, if  , then and .