205k views
5 votes
Use a proof by contradiction to prove that the sum of two odd integers is even CM

User Easythrees
by
5.6k points

1 Answer

7 votes

Answer:

Sum of two odd integers is always even.

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.

User Birey
by
5.6k points