SOLUTION: Hello, I need help with these proofs. I believe they are propositional logic and require rules 1-13 involving everything from Modus Ponens to Double Negation. 1. Gv(R&E) 2. (G

Algebra ->  Algebra  -> Proofs -> SOLUTION: Hello, I need help with these proofs. I believe they are propositional logic and require rules 1-13 involving everything from Modus Ponens to Double Negation. 1. Gv(R&E) 2. (G      Log On

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Question 201425: Hello, I need help with these proofs. I believe they are propositional logic and require rules 1-13 involving everything from Modus Ponens to Double Negation.
1. Gv(R&E)
2. (GvE)>~R
conclusion: GvM
using rules of replacement and inference.
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one way to do it: 

1.   G v (R & E)
2.   (G v E) -> ~R              :.  G v M
------------------------------------------
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