SOLUTION: Solve please. 1. ~S->(~Gv~F) 2. (~F->~W).W :. Sv~G

Algebra ->  Proofs -> SOLUTION: Solve please. 1. ~S->(~Gv~F) 2. (~F->~W).W :. Sv~G      Log On


   

Question 249373: Solve please.
1. ~S->(~Gv~F)
2. (~F->~W).W
:. Sv~G
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to use '&' instead of '.' 

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