Question 1031400: ∼S⊃(N⊃T)
~S∙(R⊃S)
(~M∙~N)⊃(~Ov~P)
(Qv~R)⊃~M
(~R∙~S)⊃(~~O∙~T) /~P
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I use to mean
& and
V or
-> material implication, aka "if...then"
~ not
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1 ~S -> (N -> T)
2 ~S & (R -> S)
3 (~M & ~N) -> (~O V ~P)
4 (Q V ~R) -> ~M
5 (~R & ~S) -> (~~O & ~T) | ~P
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6 ~S 2. Conjunction Elimination
7 R -> S 2. Conjunction Elimination
8 ~R 6, 7. Modus Tollens
9 ~R & ~S 6, 8. Conjuction Introduction
10 ~~O & ~T 5, 9. Modus Ponens
11 ~~O 10. Conjunction Elimination
12 N -> T 1, 6. Modus Ponens
13 ~T 10. Conjunction Elimination
14 ~N 12, 13. Modus Tollens
15 Q V ~R 8, Disjunction Introduction
16 ~M 4, 15. Modus Ponens
17 ~M & ~N 14, 15. Conjunction Introduction
18 ~O V ~P 3, 17. Modus Ponens
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19 :. ~P 11, 18. Disjunctive Syllogism
John
My calculator said it, I believe it, that settles it
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