Question

consider the statement if two whole numbers are even then their sum is odd.

Answer 1

It is false. The sum of of any two even whole numbers are even.

Answer 2

Any even number can be written in the form of 2n, where n is an integer. Any odd number can be written in the form 2n + 1, again n an integer. So if you have 2 even numbers, let's say 2n and 2k, n and k integers, then 2n + 2k = 2(n+k). Since the integers are closed under addition, n + k is equal to some integer and thus we get another even number.