Chapter 4, Problem 1NT

NOW TRY THIS

For any whole numbers $a\text{ and }b$, determine the truth of the statement: If $5\cancel{|}a$ and $5\cancel{|}b$, then $5\cancel{|}\left(a+b\right)$.

To determine

To explain:

The truth of the statement that if $5$ doesn’t divide $a$ and also $5$ doesn’t divide $b$, then $5$ doesn’t divide $a+b$.

Answer to Problem 1NT

Solution:

No, this statement is not true as 5 doesn’t divide $6$ and also $5$ doesn’t divide $4$ but $5$ divides $6+4=10$.

Explanation of Solution

Given:

The statement if $5$ doesn’t divide $a$ and also $5$ doesn’t divide $b$, then $5$ doesn’t divide $a+b$.

Approach:

By taking a example which is contradictory to statement given above to disprove the result.

Calculation:

As 5 doesn’t divide $6$ and also $5$ doesn’t divide $4$ but $5$ divides $6+4=10$.

So, the statement is not true that if $5$ doesn’t divide $a$ and also $5$ doesn’t divide $b$, then $5$ doesn’t divide $a+b$.