Let x and y be two odd numbers.
Then x = 2k + 1 for some natural number and y = 2l + 1 for some natural number l.
Adding x and y, we get :
⇒ x + y = 2k + 1 + 2l + 1
= 2k + 2l + 2
= 2(k + l + 1).
We know that,
Any natural number on multiplying by 2 is an even number.
Hence, proved that the sum of two odd numbers is even.