SOLUTION: Please help me with this problem for proofs: 1. A-> ~(B ->G) 2. A v G / A<-> ~G I'm thinking there will be some Hypothetical syllogism to find the conclusion. I am really

Question 194331: Please help me with this problem for proofs:
1. A-> ~(B ->G)
2. A v G / A<-> ~G
I'm thinking there will be some Hypothetical syllogism to find the conclusion. I am really bad at this thought, so I am uncertain. Please help me! I really appreciate it. Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.   A -> ~(B -> G)
2.   A v G    / A <-> ~G
-----------------------
3.  ~A v ~(B -> G)                   1     Material Implication
4.  ~A v ~(~B v G)                   3     Material Implication
5.  ~A v (~~B & ~G)                  4     DeMorgan's Theorem
6.  ~A v (B & ~G)                    5     Double Negation
7.  (~A v B) & (~A v ~G)             6     Distribution
8.  (~A v ~G) & (~A v B)             7     Commutation
9.  ~A v ~G                          8     Simplification
10. A -> ~G                          9     Material Implication
11. G v A                            2     Commutation
12. ~~G v A                         11     Double Negation
13. ~G -> A                         12     Material Implication
14. (A -> ~G) & (~G -> A)        10,13     Conjunction
15. A <-> ~G                        14     Material Equivalence

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