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Indirect Proofs

  1. Nov 30, 2005 #1
    use the method of indirect proof. if m and n are integars and there product mn is odd, prove that both m and n are odd

    so i wnat to prove that (m)(n) odd (mn)

    so i assume that (mn) is even to go about the indirect method

    now i need a jump start i wrote some equations and some algebra but dindt come up with a contradication

    help is appreciative thats alot guys
     
  2. jcsd
  3. Nov 30, 2005 #2

    Pyrrhus

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    Start off by

    [tex] m = 2k+1 [/tex]

    [tex] n = 2c + 1 [/tex]

    where k and c is any natural number.
     
  4. Dec 1, 2005 #3

    Galileo

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    Using contradiction (indirect proof), you can assume either m or n to be even (that is, a multiple of two) and show that mn must also be even.
     
  5. Dec 1, 2005 #4

    HallsofIvy

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    No, that's exactly the wrong thing to do.

    Since blimkie wants to use indirect proof to prove that "both m and n must be odd, he should negate that: "either m or n is even".

    So assume m= 2p, which is even for any integer p, multiply by n and see what happens!
     
    Last edited: Dec 4, 2005
  6. Dec 1, 2005 #5
    A number to be even it should be divisible by 2. thus for the product mn to be divisible by 2 any of the integers m or n must be divisible by prime 2. thus the divisibility testdiectlygives you the answer that then anyone of them must be an even number.
     
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