SOLUTION: I am working on proofs for my logic homework. Here are the premises: 1. ~S -> (~G v ~F) 2. (~F -> ~W) & W Here is the conclusion: S v ~G

Question 248098: I am working on proofs for my logic homework.
Here are the premises:
1. ~S -> (~G v ~F)
2. (~F -> ~W) & W
Here is the conclusion:
S v ~G
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.  ~S -> (~G v ~F)
2.  (~F -> ~W) & W          / :. S v ~G
----------------------------
3.  ~~S v (~G v ~F)             1       Material Implication
4.  S v (~G v ~F)               3       Double Negation
5.  (S v ~G) v ~F               4       Association
6.  ~F v (S v ~G)               5       Commutation
7.  F -> (S v ~G)               6       Material Implication
8.  W & (~F -> ~W)              2       Commutation
9.  W                           8       Simplification
10. ~~W                         9       Double Negation
11. ~F -> ~W                    2       Simplification
12. ~~F                         11,10   Modus Tollens
13. F                           12      Double Negation
14. S v ~G                      7,13    Modus Ponens

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