SOLUTION: if p is true, q is false, and r is true, find the truth value of the statement (~p ^ q <-> ~r)

Question 594888: if p is true, q is false, and r is true, find the truth value of the statement (~p ^ q <-> ~r)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Simply plug in the given truth values and evaluate.

Keep in mind the following rules
1) ~p is the opposite of p. So if p is true, then ~p is false. This applies in the other direction. So if p is false, then ~p is true.

2) p ^ q is only true if BOTH p and q are true. Otherwise, it's false.

3) p <--> q is only true if both truth values of p and q are the same.

So let's use these facts to get:

(~p ^ q) <-> ~r

(~T ^ F) <-> ~T

(F ^ F) <-> F

F <-> F

T

So (~p ^ q) <-> ~r is true.
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