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Math Help - laws of logic question

  1. #1
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    laws of logic question

    hey guys, i have this question.

    (((p \rightarrow r ) \rightarrow p ) \wedge q ) \wedge (-((p \rightarrow r ) \rightarrow p ))

    my answer after simplifing boths sides i got

     (p \wedge q ) \wedge (-p)

    which then using associative law gives

     q \wedge ( p \wedge -p )

    then inverse law

     q \wedge T

    then Annihilation law

     T

    so this is a tautology. Can anyone confirm this is correct? thanks!
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  2. #2
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    You lost me at your "inverse law" step. Does that big "T" mean p and not p is true for all values of p?
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  3. #3
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    Quote Originally Posted by ANDS! View Post
    You lost me at your "inverse law" step. Does that big "T" mean p and not p is true for all values of p?
    I think i just made a mistake. Its ment to be  F not T

    so that would make the final answer  F , so its a contradiction.. ?
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  4. #4
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    It would be a contradiction if this were an actual proof and you implied something (namely that it is not the case that if p then r implies p). All I see is that this is false for all values of p, q, and r, since p and not p can never be true.

    At least you recognize contradiction here, and you deduced (or I assume you did) that if p then r implies p.
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