Direct Proof Example : If n is even, then n + 1 is odd

This will be the first example we will encounter as this expedition for finding out the truth of many mathematical and logical mysteries on our journey into the realm of unsolvable problems.
Our first problem is:
Prove: If n is even, then n + 1 is odd

Proof: (Direct)
Assume n is even, therefore n has the form of an even integer which is 2k, and k is any integer.

Calculate:
n = 2k
add one to both sides
n + 1 = 2k + 1
by definition 2k + 1 is an odd integer and it equals n + 1

Conclusion:
This direct proof has shown that if n is even then n + 1 must be odd.

I have posted the indirect proof that rounds off this simple proof that wets our appetite for knowledge.