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Math Help - [SOLVED] Proving a theorem without using contradiction

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    [SOLVED] Proving a theorem without using contradiction

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    Last edited by racewithferrari; November 19th 2009 at 10:00 AM.
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    Quote Originally Posted by racewithferrari View Post
    The following theorem has the form of an implication.
    If n is an integer and 3n+2 is even, then n is even.
    Suppose that 3n+2=2k then 3n=2k-2.
    What does that tell you?
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    Quote Originally Posted by racewithferrari View Post
    The following theorem has the form of an implication.

    If n is an integer and 3n+2 is even, then n is even.

    Give a direct proof of this theorem without using contradiction.
    Since 3n+2 is even we may state WLOG that 3n+2=2z\implies 3n=2(z-1) and since 2\nmid 3 it must be true that 2\mid n. The conclusion follows.
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