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28 March, 08:48

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

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  1. 28 March, 10:24
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    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.
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