Question 249372: I need to solve this conditional proof and I can't. Help?
1. ~(M.~L)->Q
:. ~L->Q
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Note: With conditional proofs, we assume the antecedent of the conclusion. In this case, we're assuming ~L which we'll denote with C.P (for conditional proof). Also, I'm going to use '&' in place of '.'
1. ~(M & ~L) -> Q / :. ~L -> Q
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2. ~L C.P.
3. ~~(M & ~L) v Q 1 Material Implication
4. (M & ~L) v Q 3 Double Negation
5. Q v (M & ~L) 4 Commutation
6. (Q v M) & (Q v ~L) 5 Distribution
7. (Q v ~L) & (Q v M) 6 Commutation
8. Q v ~L 7 Simplification
9. ~~Q v ~L 8 Double Negation
10. ~Q -> ~L 9 Material Implication
11. ~L v ~L 2 Addition
12. ~~L v ~L 11 Double Negation
13. L -> ~L 12 Material Implication
14. ~L -> ~~L 13 Transposition
15. ~L -> L 14 Double Negation
16. ~Q -> L 10,15 Hypothetical Syllogism
17. ~L -> ~~Q 16 Transposition
18. ~L -> Q 17 Double Negation
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