Discrete mathematics: Please provide an explanation for your solution, as well.

6. Quietly Ending Debate (20 points) Recall that an integer n is even iff there exists an integer a such that n 2a, and it is odd iff there exists an integer a such that n 2a 1 (a) [12 Points] Give a formal proof that, if n is odd and m is even, then n+m is odd. In addition to the rules given in class, you can also rewrite algebraic expressions to equivalent ones using the rule "Algebra." (b) [8 Points] Write your proof from part (a) as an English proof