Question

suppose a and b are positive integers. Prove if a – b is odd, then a + b is odd.

Answer 1

if the difference of two number is odd, then one is even and the other odd
therefore the sum must be odd

Answer 2

or you can say if \(a-b\) is odd, then \((a-b)+(a+b)=2a\) is even making \(a+b\) odd

Answer 3

you can probably do even better on your own
i am sure there are lots of ways to do this