Question

Use a proof by contradiction to prove that the sum of two odd integers is even CM

Answer 1

Answer:

Sum of two odd integers is always even.

Step-by-step explanation:

Let m and n be two odd integers.

Since m and n are odd they can be written in the form m =2r + 1 and n = 2s + 1, where r and s are integers.

Let us suppose that their sum is not even.

m + n = (2r+1) + (2s + 1)

          = 2r + 2s + 2

          = 2(r+s+1)

          = 2z

Thus, the sum of m and n can be written in the form 2z where z is an integer. But this is a contradiction to the fact that their sum is even.

Hence, our assumption was wrong and the sum of two odd integers is always even.