Question 1006581: Q∨P
R→~P
R→Q
Here is what I put but I have not been able to pass correctly. Feedback is the proof solution is wrong. Any help would be great.
Solution
1) Q∨P
2) R→~P
3) Q (SIMP 1)
4) P (SIMP 2)
5) R (MP 2, 4)
6) R→Q (HS 3, 5)
Simplifying 1, we derive lines 3 and 4. Line 5 comes about as a natural deduction of line 2 and 4. Using DS rule, we derive line 6 from line 3 and 5.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Simplification only works if you have a conjunction. NOT a disjunction.
Here is how to do the derivation
1) Q v P (given premise)
2) R -> ~P (given premise)
:. R -> Q (what we want to derive)
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3) P v Q (1, commutation)
4) ~~P v Q (3, double negation)
5) ~P -> Q (4, Material Implication)
6) R -> Q (2,5, hypothetical syllogism)
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