Exercise 2.7.2: Proofs by cases - even/odd integers and divisibility. About Prove each statement. (a) If is an integer, then is odd. Solution (b) If integers and have the same parity, then is even. The parity of a number tells whether the number is odd or even. If and have the same parity, they are either both even or both odd. (c) If integers and where are consecutive, then they have opposite parity. (d) For integers and , if is odd, then is odd and is odd.