**Problem:**Prove: The sum of two even integers is even. Use a Direct Proof.

**The Proof:**

Code: Select all

`a + b even integers`

a = 2n

b = 2m

a + b = 2n + 2m

a + b = 2(n + m)

Supposedly it is now proven. I do not get this at all, here are some questions:

1. Why do we set a and b to 2n and 2m?

2. Why the 2 at all?

3. What

**exactly**is m and n?

4. How does 2(n + m) prove this question true at all? For example, how can I do a check using the proof to see some true outcomes?