Question

Prove that the sum of two odd numbers is an even number

Answer 1

Let a and b be odd number.
Because they are odd, by definition:
a = 2n + 1 
b = 2m + 1
If we add them up:
a + b = 2n + 1 + 2m + 1
         = 2n + 2m + 2
         = 2(n + m + 2)
         = 2k where k = n + m + 2

therefore a + b is always even.