28 March, 08:48
Use a proof by contradiction to prove that the sum of two odd integers is even CM
28 March, 10:24
Sum of two odd integers is always even.
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)
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.
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