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Math Help - Logical Equivalence

  1. #1
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    Feb 2008
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    13

    Logical Equivalence

    Could someone please help me with these two questions
    I have trouble solving it.
    Any help would be appreciated.
    Thanks for answering!
    Attached Thumbnails Attached Thumbnails Logical Equivalence-discretef.bmp  
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  2. #2
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    Joined
    Aug 2008
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    [(p\lor q)\land (p\to r)\land (q\to r)]\to r
    =
    [(p\lor q)\land (\lnot p\lor r)\land (\lnot q\lor r)]\to r
    =
    \{(p\lor q)\land [(\lnot p\land \lnot q)\lor r]\}\to r
    =
    \{(p\lor q)\land [\lnot (p\lor q)\lor r]\}\to r
    =
    \{(p\lor q)\land [(p\lor q)\to r]\}\to r

    the last one is the tautology of modus ponens rule
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