DISCRETE MATHS

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If m and n are integers such that mn is even, then m is even or n is even.

how can i prove this using contraposition?

  • DISCRETE MATHS -

    if both are odd, we can let

    m = 2a+1
    n = 2b+1

    mn = (2a+1)(2b+1) = 4ab+2a+2b+1
    so, mn is odd if m and n are both odd.

    So, if mn is even, then m and n cannot both be odd.

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