SOLUTION: Prove the following: 1. O --> (H * M) 2. (O --> G) --> (H --> ~M) 3. ~G --> (~H v ~M) .·. H --> ~M

Algebra ->  Proofs -> SOLUTION: Prove the following: 1. O --> (H * M) 2. (O --> G) --> (H --> ~M) 3. ~G --> (~H v ~M) .·. H --> ~M       Log On


   

Question 1171292: Prove the following:
1. O --> (H * M)
2. (O --> G) --> (H --> ~M)
3. ~G --> (~H v ~M) .·. H --> ~M

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1.  O --> (H * M)
2.  (O --> G) --> (H --> ~M)
3.  ~G --> (~H v ~M)                 .·. H --> ~M

4.  ~(~H v ~M) --> ~~G         3, Transposition
5. (~~H * ~~M) --> ~~G         4, DeMorgan's Law
6. (H * M) --> G               5, Double Negation
7. O --> G                     1,6, Hypothetical Syllogism 
8. H --> ~M                    2,7, Modus Ponens

Edwin