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Math Help - How to prove an IFF (If and only If) statement!

  1. #1
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    How to prove an IFF (If and only If) statement!

    How would you go about proving these:

    1)

    For all integers n, n is even if and only if n -1 is odd


    2)

    if d|(a+b) and d|a, where a,b and d are integers, d is not equal to 0
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  2. #2
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    Re: How to prove an IFF (If and only If) statement!

    Suppose n is even then n = 2m for some m.
    therefore n = 2m
    obviously n-1=2m - 1 is odd
    Alternatively
    if n- 1 is odd then (n-1) + 1 = is n which is even for n-1 is odd.
    we can also say that for n-1 being odd implies em-1 is odd where n = 2m for some m.
    thus (n-1) = (2m-1)-1 = 2m-2 = 2(m-1) which is even.
    Hence the proof
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