SOLUTION: If(~P->Q)->(PvR)is false, what are the truth values of P,Q and R?

Question 981453: If(~P->Q)->(PvR)is false, what are the truth values of P,Q and R?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
(~P->Q)->(PvR)is false

So (~P->Q) is true while (PvR) is false. The generic form X->Y is only false if X is true but Y is false.
-------------------------------------------------------
Since (PvR) is false this means that both P and R have to be false. Otherwise, (PvR) would be true.

P is false, so ~P is true.

-------------------------------------------------------

~P is true and (~P->Q) is true. So Q has to be true. If Q were false, then (~P->Q) would be false.

=======================================================

So

P = false
Q = true
R = false
RELATED QUESTIONS
P is True, q and r are False- find the truth value. a) (p ^ ~q) ^ r b)... (answered by Edwin McCravy)

Please help! determine the truth value of the statement when p is T, q is F, and r is... (answered by jim_thompson5910)

I have being given to solve Find the truth value of (P ⇒ Q) ∨ R if P is... (answered by Edwin Parker)

if p is true and q is false and r is true what is the truth statement of the statement ~[ (answered by lynnlo)

if p is false and q is true, what is the truth for... (answered by user_dude2008)

Determine the truth value of the statement ~q <-> [ ~ r ^ (p v q)] when p is false, q is... (answered by Edwin McCravy)

HELP Determine the truth value of the statement ~q arrow [ ~ r v (revered) (p v q)]... (answered by MathLover1)

Determine the truth value of the statement ~q <-> [~ r ~ (p ^ q)] when p is false, q is... (answered by Edwin McCravy)

If p is true, q is true, and r is false, then the truth value of ~[~(p^r) V ~q] is ?... (answered by jim_thompson5910)