SOLUTION: ∼A∙~B ~D⊃A M⊃[(NvO)⊃P] Q⊃(SvT) (~Qv~R)⊃(M∙N) ~Dv~(SvT) ∴P∙~B

Algebra.Com
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!
NumberStatementLines UsedReason
1~A & ~B
2~D -> A
3M -> [(N v O) -> P]
4Q -> (S v T)
5(~Q v ~R) -> (M & N)
6~D v ~(S v T)
:.P & ~B
7~B & ~A1Commutation
8~A1Simplification
9~B7Simplification
10~~D2,8Modus Tollens
11~(S v T)6,10Disjunctive Syllogism
12~Q4,11Modus Tollens
13~Q v ~R12Addition
14M & N5,13Modus Ponens
15N & M14Commutation
16M14Simplification
17N15Simplification
18N v O17Addition
19(N v O) -> P3,16Modus Ponens
20P19,18Modus Ponens
21P & ~B20,9Conjunction
RELATED QUESTIONS

∼S⊃(N⊃T) ~S∙(R⊃S) (~M∙~N)⊃(~Ov~P)... (answered by solver91311)
Could you please help me? Im sick with a bug and cant think straight :/ A) 1. A ⊃ (answered by solver91311)
P∙ Q R⊃ ~Q / ~R∨ ~P (answered by jim_thompson5910)
Please help! A ⊃ B A ⊃ (B ⊃ C) B ⊃ (C ⊃ D) ∴ A... (answered by Edwin McCravy)
(M ∨ R) ⊃ ∼K (G ⊃ ∼K) ⊃ C G ⊃ (M ∨ R) (answered by solver91311)
How do I complete the following proofs? Premises: 1. L ⊃ M 2. L 3. K v Q... (answered by Edwin McCravy)
construct a formal proof of validity for the following argument. 1. (M ⊃ N)... (answered by Edwin McCravy)
Please help me create this proof using the 18 rules of inference. I have been working on... (answered by jim_thompson5910)
Give reasons for the steps, given premises 1, 2 and 3:

1.  X ⊃ (Y ⊃  (answered by Edwin McCravy)