Question

Prove that if n is an even integer, then n + 1 is odd. Give a proof by contraposition of this theorem.

Answer 1

Proved below

Explanation:

If we assume that n + 1 even when n is even, it means that;

n + 1 = 2x

Where x is an integer

Then;

n = 2x - 1

This means that n is odd because 2x - 1 is odd.

But we know that n is even, thus, our assumption is wrong.

Therefore, n + 1 is odd when n is even.