SOLUTION: I have started the following proof but am not sure how to finish. thanks! 1. G>(H>K) 2. (Hv~M) > ~K 3. H // ~G 4. ~Gv(H>K) >equals horseshoe

Question 607205: I have started the following proof but am not sure how to finish. thanks!
1. G>(H>K)
2. (Hv~M) > ~K
3. H // ~G
4. ~Gv(H>K)
>equals horseshoe
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.   G -> (H -> K)
2.   (H v ~M) -> ~K
3.   H 
-------------------------------------------------------
4.   H v ~M                          3        Addition
5.   ~K                              2,4      Modus Ponens
6.   (G * H) -> K                    1        Exportation
7.   ~(G * H)                        6,5      Modus Tollens
8.   ~G v ~H                         7        De Morgan's Law
9.   ~H v ~G                         8        Commutation
10.  ~~H                             3        Double Negation
11.  ~G                              9,10     Disjunctive Syllogism

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