SOLUTION: Prove that the two arguments below are valid, using the method of natural deduction. Use the rules of implication and rules of replacement 1. B -> (D -> H) 2. ~(D -

Algebra ->  Proofs -> SOLUTION: Prove that the two arguments below are valid, using the method of natural deduction. Use the rules of implication and rules of replacement 1. B -> (D -> H) 2. ~(D -      Log On


   

Question 1022622: Prove that the two arguments below are valid, using
the method of natural deduction. Use the rules of
implication and rules of replacement
1. B -> (D -> H)
2. ~(D -> ~B) // H
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1.      B -> (D -> H)
 2.      ~(D -> ~B)               //        H

 3.      (B v D) -> H        1, Importation
 4.      ~(~D v ~B)          2, Material implication
 5.      ~~D & ~~B           3, DeMorgan's law
 6.      D & B               4, Double negation
 7.      B & D               6, Commutation 
 8.      B                   7, Simplification
 9.      B v D               8, Addition
10.      H                   3,9, Modus Ponens

Edwin