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Math Help - tautology/logic help

  1. #1
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    tautology/logic help

    I have a problem that says prove that p^(p exclusive or q) --> (p-->q) is NOT a tautology. I've tried converting both conditional statements into ~p v q but I still get a tautology.

    Do I use truth tables to prove that this isn't a tautology? If not by what other means. Or did I just make a mistake somewhere?
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  2. #2
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    Quote Originally Posted by guyonfire89 View Post
    I have a problem that says prove that p^(p exclusive or q) --> (p-->q) is NOT a tautology. I've tried converting both conditional statements into ~p v q but I still get a tautology.
    Suppose that P\text{ is true and }Q\text{ is false } .
    Then P \wedge \left( {P\underline  \vee  Q} \right) \text{ is true } ~ but ~P \to Q \text{ is false }
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    thanks but I don't understand how P ^ (P xor Q) is true.
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    Quote Originally Posted by guyonfire89 View Post
    thanks but I don't understand how P ^ (P xor Q) is true.
    P \oplus Q \equiv (P\land\neg Q) \lor(\neg P\land Q)
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    Quote Originally Posted by guyonfire89 View Post
    thanks but I don't understand how P ^ (P xor Q) is true.
    \left( {P\underline  \vee  Q} \right) \equiv \left( {P \wedge \neg Q} \right) \vee \left( {\neg P \wedge Q} \right)
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  6. #6
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    Quote Originally Posted by undefined View Post
    P \oplus Q \equiv (P\land\neg Q) \lor(\neg P\land Q)
    Quote Originally Posted by Plato View Post
    \left( {P\underline  \vee  Q} \right) \equiv \left( {P \wedge \neg Q} \right) \vee \left( {\neg P \wedge Q} \right)
    Thanks. My teacher never mentioned that in class. Makes a lot more sense
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