Prove that the sum of two odd numbers is even.

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.