Question

Let a and b be any two integers. Show that the following statement is false: If 3|(a+b),then 3|(a−b).Hint. To show that the statement is false, you need to find two integers a and b for which 3|(a+b) is true and 3|(a−b) is false.

Answer 1

Answer with Step-by-step explanation:

Let a and b are two integers.

We have to show that

if 3\a+b then 3\a-b is false.

In order to prove that given statement is false we prove this with the help of example

Suppose we have two integers a=2 and b=4

if 3\2+4

3\6=2

2-4=-2

But 3 does not divide -2.

Therefore, the given statement is false.

Hence, proved.