SOLUTION: Natural Deduction How do I solve the proof: 1. (Av~B)⊃((A•C)⊃B) 2. ~B /A⊃~C

Algebra ->  Proofs -> SOLUTION: Natural Deduction How do I solve the proof: 1. (Av~B)⊃((A•C)⊃B) 2. ~B /A⊃~C      Log On


   

Question 1028652: Natural Deduction
How do I solve the proof:
1. (Av~B)⊃((A•C)⊃B)
2. ~B /A⊃~C
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

1. (Av~B)⊃[(A+C)⊃B]
2. ~B              /  A⊃~C

3. [(Av~B)•(A&C)]⊃B          1, Importation
4. ~[(Av~B)•(A•C)]           3,2 Modus Tollens
5. ~(Av~B)v~(A•C)            4, DeMorgan's law
6. ~BvA                      2, Addition
7. Av~B                      6, Commutation
8. ~~(Av~B)                  7, Double negation
9. ~(A•C)                    5,8, Disjunctive syllogism
10. ~Av~C                    9, DeMorgan's law
11. A⊃~C                     10, Material implication

Edwin