Question 472504: PLEASE HELLPP!!! Given p is false, q is true, and r is false, find the truth value of the statement (~p ↔ ~q) ~r.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! If p is true, then ~p is false (since ~p is the opposite of p).
Remember that "^" means "and". The statement p ^ q is only true if BOTH p AND q are true (hence the "and"). Since ~p is false, we automatically know that ~p ^ q is false (q doesn't have to be factored in at all).
Finally, remember that p <-> q is only true if the truth values for p and q are the same. So if p and q are both true, or both false, then p <-> q is true. Think of this as an "equals" (ie p = q). Because r is true, ~r is false. Since ~p ^ q is false as well, ~p ^ q and ~r have the same truth values. So (~p ^ q) <-> ~r is true.
Here's one way you could write all this out:
(~p ^ q) <-> ~r
(~T ^ F) <-> ~T
(F ^ F) <-> F
F <-> F
T
Answer by jim_thompson5910
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