Question 1031401: ∼A∙~B
~D⊃A
M⊃[(NvO)⊃P]
Q⊃(SvT)
(~Qv~R)⊃(M∙N)
~Dv~(SvT) ∴P∙~B
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
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| 1 | ~A & ~B | | | | 2 | ~D -> A | | | | 3 | M -> [(N v O) -> P] | | | | 4 | Q -> (S v T) | | | | 5 | (~Q v ~R) -> (M & N) | | | | 6 | ~D v ~(S v T) | | | | :. | P & ~B | | | | 7 | ~B & ~A | 1 | Commutation | | 8 | ~A | 1 | Simplification | | 9 | ~B | 7 | Simplification | | 10 | ~~D | 2,8 | Modus Tollens | | 11 | ~(S v T) | 6,10 | Disjunctive Syllogism | | 12 | ~Q | 4,11 | Modus Tollens | | 13 | ~Q v ~R | 12 | Addition | | 14 | M & N | 5,13 | Modus Ponens | | 15 | N & M | 14 | Commutation | | 16 | M | 14 | Simplification | | 17 | N | 15 | Simplification | | 18 | N v O | 17 | Addition | | 19 | (N v O) -> P | 3,16 | Modus Ponens | | 20 | P | 19,18 | Modus Ponens | | 21 | P & ~B | 20,9 | Conjunction |
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