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Math Help - truth tables

  1. #1
    Newbie
    Joined
    Aug 2006
    Posts
    5

    Smile truth tables

    (p->q)->(p^q)
    Write down its truth table
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  2. #2
    Member
    Joined
    Jun 2006
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    San Diego
    Posts
    101
    Well P and Q are the only statement variables, so there are four possible inputs:
    P true, Q true; P true, Q false; P false, Q true; and P false, Q false.

    So you'll need four rows.
    The statement is (P->Q) -> (P^Q)
    If you let C = P->Q and D = (P^Q) then this is really just C->D, which is elementary.

    Code:
                 C          D
    P    Q     (P->Q)     (P^Q)    C->D
    -------------------------------------
    T    T       T          T         
    T    F       F          F
    F    T       T          F   
    F    F       T          F
    The final column, which is the one continaing the truth possibilities for the given statement, I will leave since it's pretty easy to finish up at this point.
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