SOLUTION: Use an ordinary proof to show the conclusion can be derived from the premises. 1. G ⊃ (H ⊃ K) 2. (H v ~M) ⊃ ~K 3. H /~G

Algebra ->  Proofs -> SOLUTION: Use an ordinary proof to show the conclusion can be derived from the premises. 1. G ⊃ (H ⊃ K) 2. (H v ~M) ⊃ ~K 3. H /~G      Log On


   

Question 1030073: Use an ordinary proof to show the conclusion can be derived from the premises.
1. G ⊃ (H ⊃ K)
2. (H v ~M) ⊃ ~K
3. H /~G
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1. G ⊃ (H ⊃ K)
 2. (H v ~M) ⊃ ~K
 3. H             /~G

 4. H v ~M            3, addition
 5. ~K                2,4, modus ponens
 6. ~(H ⊃ K) ⊃ ~G    1, transposition
 7. ~(~H v K) ⊃ ~G   6, Material implication
 8. (~~H • ~K) ⊃ ~G  7, DeMorgan's law
 9. (H • ~K) ⊃ ~G    8, Double negation
10. H • ~K           3,5 Conjunction
11. ~G               9,10, Modus ponens  

[Note some teachers and books use & instead of •, 
while others use ∧ ]
 
Edwin