SOLUTION: 1. (N v M) > (P & O) 2. ~M > (~Q

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Question 1061182: 1. (N v M) > (P & O)
2. ~M > (~Q > Q)
3. ~O
/Q
Answer by jim_thompson5910(35256) (Show Source):
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Number Statement Lines Used Reason
1 (N v M) > (P & O)
2 ~M > (~Q > Q)
3 ~O
:. Q
4 ~(N v M) v (P & O) 1 MI
5 [~(N v M) v P] & [~(N v M) v O] 4 Dist
6 [~(N v M) v O] & [~(N v M) v P] 5 Comm
7 ~(N v M) v O 6 Simp
8 O v ~(N v M) 7 Comm
9 ~(N v M) 8,3 DS
10 ~N & ~M 9 DM
11 ~M & ~N 10 Comm
12 ~M 11 Simp
13 ~M > (~~Q v Q) 2 MI
14 ~M > (Q v Q) 13 DN
15 ~M > Q 14 Taut
16 Q 15,12 MP

Abbreviations/Acronyms used:

Comm = Commutation
Dist = Distribution
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
MI = Material Implication
MP = Modus Ponens
Simp = Simplification
Taut = Tautology

SOLUTION: 1. (N v M) > (P & O) 2. ~M > (~Q > Q) 3. ~O /Q