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

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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):
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(~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.
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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.

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

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So

P = false
Q = true
R = false