Two integers have the same parity if both are even or both a

Two integers have the same parity if both are even or both are odd. Otherwise they have opposite parity.

Let a,b Z. Show that if a + b is even, then a,b have the same parity.

Hint: Use a contrapositive proof.

Let a,b have the opposite parity, then one of them is even and one of them is odd.

As a integer can be even or odd.

Now sum of an even integer and an odd integer is an odd integer, that is a+b is odd

But its given that a + b is even.

Hence by contrapositive, we have if a + b is even, then a,b have the same parity