Question

Prove that if two integers have opposite parity their sum is odd?

Answer 1

Refer explanation.

Explanation:

If two integers have opposite parity, prove their sum is odd.

Ex.

`1 + 2 = 3`

`1` is considered as odd number while `2` is considered as even number and `1` & `2` are integers that have opposite parity which produces a sum of `3` which is an odd number.

Ex. `2`

`131+156 = 287`

Odd + Even = Odd

`:. Proven`

Answer 2

See below.

Explanation:

Let `n` be any integer:

Then:

`2n` is a even integer and `2n+1` is an odd integer:

There sum:

`2n+2n+1=4n+1=2(2n)+1`

Hence `4n` is even, so `4n+1` is odd.