(Solved): Discrete Math 2. (8 pt) Two integers have the same parity if and only if they are both even or both ...

2. (8 pt) Two integers have the same parity if and only if they are both even or both odd. Give an outline rather than a complete proof for how to prove the following biconditional: For all integers \( m \) and \( n, m^{3}-n^{2} \) is even if and only if \( m \) and \( n \) have the same parity. (1) What statement or statements should be proved? (2) What combination of proof methods you would use to prove the statement or statements given in (1)? Proof methods include Direct Proof, Proof by Cases, Proof by Contradiction, and Proof by Contraposition.