SOLUTION: I need to solve this conditional proof and I can't. Help? 1. ~(M.~L)->Q :. ~L->Q

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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
-------------------------
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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