# Abstract Math, Tautology

1. Aug 30, 2010

### joemama69

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. Aug 30, 2010

Note: ~(P v Q) is equivalent to (~P and ~Q). So your sample statement S does not work.

3. Aug 30, 2010

### joemama69

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