SOLUTION: How do you come to the conclusion of ~G given the following premises 1. G->(H->K) 2.(Hv~M)->~K 3. H Key: "->" means horseshoe (material implication) "v" means wedge (di

Algebra ->  Proofs -> SOLUTION: How do you come to the conclusion of ~G given the following premises 1. G->(H->K) 2.(Hv~M)->~K 3. H Key: "->" means horseshoe (material implication) "v" means wedge (di      Log On


   

Question 607197: How do you come to the conclusion of ~G given the following premises
1. G->(H->K)
2.(Hv~M)->~K
3. H
Key: "->" means horseshoe (material implication)
"v" means wedge (disjucntion)
Answer by jim_thompson5910(35256) About Me  (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