# Logic - Truth Tables, DeMorgan's Laws.

1) Construct a truth table and determine the truth value of the statement

~ q = { ~r ^ ( p v q) }, when p is false, q is true and r is true.

2) Use De Morgan's Laws to determine whether the two statements are equivalent. ~( p ^ q), ~(q v ~p)

3) Determine which, if any of the three statements are equivalent.

a) If today is Monday, then tomorrow is not Wednesday

b) It is false that today is Monday and tomorrow is not Wednesday

c) today is not Monday or tomorrow is Wednesday.

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#### Solution Preview

1) Construct a truth table and determine the truth value of the statement

~ q => { ~r ^ ( p v q) }, when p is false, q is true and r is true.

Since there are 3 simple statements p, q and r, there will be 2^3 = 8 possible combinations of the truth values of p, q and r. The truth table is shown ...

#### Solution Summary

Detailed solutions with Truth Tables are provided.