### Prove that n2-n is even for every positive integer n.

Step by Step Explanation:
1. We have been asked to prove that n2 - n is even for every positive integer n.
2. Before beginning, we have to understand the following
Even × Even = Even
Even - Even = Even
Odd - Odd = Even
Odd × Odd = Odd
3. First, suppose n is odd:
Now, n2 - n = (odd)2 - (odd)
= odd × odd - odd
= odd - odd
= Even
4. Second, suppose n is even:
Now, n2 - n = (even)2 - (even)
= even × even - even
= even - even
= even
5. Therefore, n2 - n is even for every positive integer n.