SOLUTION: Given the argument: 1. G⊃(H⊃K) 2.(H∨∼M)⊃∼K 3. H /∼G Identify the rules of replacement/inference used to derive the proposition: (G • H) ⊃ ~K?

Algebra ->  Proofs -> SOLUTION: Given the argument: 1. G⊃(H⊃K) 2.(H∨∼M)⊃∼K 3. H /∼G Identify the rules of replacement/inference used to derive the proposition: (G • H) ⊃ ~K?       Log On


   

Question 1207644: Given the argument:
1. G⊃(H⊃K)
2.(H∨∼M)⊃∼K
3. H /∼G
Identify the rules of replacement/inference used to derive the proposition: (G • H) ⊃ ~K?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Given the argument:
1. G ⊃ (H ⊃ K)
2.(H ∨ ∼M) ⊃ ∼K
3. H        / ∼G

4. H ∨ ∼M          3, Addition  
5. ~K               2, Modus ponens
6. (G • H) ⊃ K     1, importation
7. ~(G • H)       6,5  Modus ponens   
8. ~G ∨ ~H          7, DeMorgan's
9. ~~H              3, Double negation
10. ~G            8,9, Disjunctive syllogism              

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Identify the rules of replacement/inference used to derive the proposition: 
(G • H) ⊃ ~K? 

Sorry, that's not true in the above case as you see by step 6. 

Edwin