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
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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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