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Math Help - Disjunctive Normal Form

  1. #1
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    Disjunctive Normal Form

    I have a question here requiring logical equivalences.

    Express (not(p v q)) ^ r in disjunctive normal form by applying logical equivalences.

    I must use logical equivalences to complete it, I cant construct a truth table.

    from the laws i know associativity says ((p v q) v r) <==> (p v (q v r)).
    and with distributivity i have (p v (q ^ r) <==> ((p v q) ^ (p v r))

    I feel like these are the laws I need to solve the problem but I just cannot seem to wrap my head around it. Can somebody please put me on the right track. Thanks.
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  2. #2
    Newbie dmitryk53's Avatar
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    Waterloo, Ontario, Canada
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    i will assume (not(p v q)) ^ r means ~(P\/Q)/\R
    so what you want to do first is bring the ~ in as so:
    (~P/\~Q)/\R
    then you want to bring the R into the (~P/\~Q) as so:
    (~P/\R)\/(~Q/\R)
    so now you have the correct form for a DNF, but do not have all the propositional variables in each OR'd section. So now add a Q to the first section and a P to the second one as so:
    (~P/\Q/\R)\/(~P/\~Q/\R)\/(P/\~Q/\R)\/(~P/\~Q/\R)
    and you're done.

    hope this helps (i know i'm a bit late, but this is my first time on this forum and i found your question through google)
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