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Is this a tautology?

  1. Sep 6, 2011 #1
    If the negation of an implication is a contradiction, the implication is a tautology.

    Is this correct? Because if the negation is never true, then it must be a tautology...No?

    For example, I am working on a problem that, after a whole bunch of other stuff, the negation of my statement is P [itex]\wedge[/itex] [itex]\neg[/itex]P [itex]\wedge\neg[/itex]Q..which is NEVER true. And because this was the negation of an implication (IE, the only time the implication is ever false), the implication is always true...
  2. jcsd
  3. Sep 6, 2011 #2
    That is correct.

    In this case, I suspect that the original implication is [itex]P\rightarrow P\vee Q[/itex]? This is indeed a tautology!
  4. Sep 6, 2011 #3
    No it was a real mess of statements. What I posted was actually just part of the final product (but that contradiction held all of the power, so to speak). I do remember something along the lines of that in it though.

    Thanks for confirming =]
  5. Sep 8, 2011 #4
    I've never quite understood what it means to be a tautology, and I suppose there cannot be an actual definition of it- any mathematical proof just uses a string of implications to provide a new implication. But I certainly wouldn't say that a,b,c,n integers, n greater than 2 means that a^n+b^n cannot be equal to c^n !!.
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