SOLUTION: Use an ordinary proof (not conditional or indirect proof): 1. G ⊃ (H ⊃ K) 2. (H ∨ ∼M) ⊃ ∼K 3. H / ∼G

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Question 1141413: Use an ordinary proof (not conditional or indirect proof):
1.
G ⊃ (H ⊃ K)

2.
(H ∨ ∼M) ⊃ ∼K

3.
H
/ ∼G
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Use an ordinary proof (not conditional or indirect proof):

1.  G ⊃ (H ⊃ K) 
2.  (H ∨ ∼M) ⊃ ∼K 
3.  H                / ∼G

4.  H ∨ ∼M         3, addition
5.  ~K             2,4 modus ponens
6.  (G ∙ H) ⊃ K    1, importation
7.  ~(G ∙ H)       6,5, modus tollens
8.  ~G ∨ ~H        7, deMorgan's law
9.  ~H ∨ ~G        8, commutation
10. ~~H ∨ ~G       3, double negation
11. ~G             9,10, disjunctive syllogism    

Edwin