Question 201425
Here's one way to do it:


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1.   G v (R & E)
2.   (G v E) -> ~R              :.  G v M
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3.   (G v R) & (G v E)              1      Distribution
4.   (G v E) & (G v R)              3      Commutation
5.   G v R                          3      Simplification
6.   G v E                          4      Simplification
7.   ~R                           2,6      Modus Ponens
8.   ~~G v R                        5      Double Negation
9.   ~G -> R                        8      Material Implication
10.  G                            9,7      Modus Tollens
11.  G v M                         10      Addition

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