SOLUTION: 1) Vv(F&G) 2) V->E 3) G->(M->I) 4) M // therefore, IvE 5) (G&M)->I 3 Exportation 6) -(G&M)vI 5 Material Implication 7) (VvF)&(VvG) 1 Distribution

SOLUTION: 1) Vv(F&G) 2) V->E 3) G->(M->I) 4) M // therefore, IvE 5) (G&M)->I 3 Exportation 6) -(G&M)vI 5 Material Implication 7) (VvF)&(VvG) 1 Distribution - = negation How do I

Question 250587: 1) Vv(F&G)
2) V->E
3) G->(M->I)
4) M // therefore, IvE
5) (G&M)->I 3 Exportation
6) -(G&M)vI 5 Material Implication
7) (VvF)&(VvG) 1 Distribution
- = negation
How do I figure out this proof?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm going to use ~ for the negation symbol

1)  V v (F & G)
2)  V -> E
3)  G -> (M -> I)
4)  M                  // therefore, I v E
--------------------------------------------
5)  (V v F) & (V v G)                     1       Distribution
6)  (V v G) & (V v F)                     5       Commutation
7)  V v G                                 6       Simplification
8)  ~~V v G                               7       Double Negation
9)  ~V -> G                               8       Material Implication
10) ~G -> ~~V                             9       Transposition
11) ~G -> V                              10       Double Negation
12) ~G -> E                              11,2     Hypothetical Syllogism
13) ~E -> ~~G                            12       Transposition
14) ~E -> G                              13       Double Negation
15) ~E -> (M -> I)                       14,3     Hypothetical Syllogism    
16) (~E & M) -> I                        15       Exportation
17) (M & ~E) -> I                        16       Commutation
18) M -> (~E -> I)                       17       Exportation
19) M -> (~~E v I)                       18       Material Implication
20) M -> (E v I)                         19       Double Negation
21) E v I                                20,4     Modus Ponens
22) I v E                                21       Commutation

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