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Math Help - tautology or not

  1. #1
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    tautology or not

    In the following formula :

     |x+y| = |x|+|y|\Longleftrightarrow (x+y\geq 0 \Longrightarrow x+y=|x|+|y|)\wedge(x+y<0\Longrightarrow x+y=-|x|-|y|)

    I substituted :

    1)|x+y|=|x|+|y| with a

    2) x+y\geq 0 with b

    3)x+y=|x|+|y| with c

    4) x+y<0 with d

    5) x+y = -|x|-|y| with e


    Then

    I tried to write the truth table of :

     a\Longleftrightarrow (b\Longrightarrow c)\wedge (d\Longrightarrow e)

    expecting to get a tautology.


    But unfortunately i did not get a tautology. Why?


    Does that mean that the above formula in not provable??
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  2. #2
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    Re: tautology or not

    Quote Originally Posted by psolaki View Post
    In the following formula :
     |x+y| = |x|+|y| \longleftrightarrow (xy)\ge 0

    I suggest you try to prove the above.
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  3. #3
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    Re: tautology or not

    Quote Originally Posted by Plato View Post
    I suggest you try to prove the above.
    To prove :

    |x+y|=|x|+|y|\Longleftrightarrow xy\geq 0 is easy, but i do not see what that has to do with my problem
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