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Homework Help: Abstract Math, Tautology

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a statement for , S, equibalten to ~(P v Q) and show that it is logically equivalent by construction the truth table for "S if and only if ~(P v Q)" and showing that this statement form is a tautology.

    2. Relevant equations

    3. The attempt at a solution

    My statment is

    S: It is not Monday or it is not tuesday.

    I'm not sure exactly how to set up the truth table. What would be my Column labels for S <-> ~(P v Q). Do in include the S or the <-> in the table.
    Last edited: Aug 30, 2010
  2. jcsd
  3. Aug 30, 2010 #2
    Note: ~(P v Q) is equivalent to (~P and ~Q). So your sample statement S does not work.
  4. Aug 30, 2010 #3
    right right right

    S:It is not monday and it is not munday ... ~(PvQ) <->(~P ^ ~Q) which are equil and because they are equal they will be a tautology.

    is it correct to say they are a tautology becasue it will be all truths in the truth table which is because ~(PvQ) and (~P ^ ~Q) have equal truths (F,F,F,T) and then because they are the same (F,F,F,T) they are then all truths for ~(PvQ) <->(~P ^ ~Q) column
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