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Logic proof

  1. Feb 21, 2005 #1
    Given that XOR is defined by [itex]((X \wedge \neg Y) \vee (\neg X \wedge Y))[/itex], in order to prove that XOR is commutative is it sufficient to prove that
    [itex]((X \wedge \neg Y) \vee (\neg X \wedge Y)) \supset ((Y \wedge \neg X) \vee (\neg Y \wedge X))[/itex]
    is a tautology?
     
  2. jcsd
  3. Feb 21, 2005 #2

    Hurkyl

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    Think about what that says:

    If (X xor Y), then (Y xor X).

    Is that the same as X xor Y = Y xor X?

    (no)

    Now, in general you would leave the last step implicit, because it's fairly routine, but I imagine you're interested in full rigor.
     
  4. Feb 21, 2005 #3
    OK, I'd like to retract that ridiculous statement before I get banned. :rofl: :rofl: :rofl:

    Maybe I'd better get some sleep... :zzz:
     
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