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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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