SOLUTION: I need help finishing this proof. A v (~B v ~C), A -> (D -> E), ~(~B v ~D) :. C -> (D -> E) 1. A v (~B v ~C) 2. A -> (D -> E) 3. ~(~B v ~D)

Algebra ->  Proofs -> SOLUTION: I need help finishing this proof. A v (~B v ~C), A -> (D -> E), ~(~B v ~D) :. C -> (D -> E) 1. A v (~B v ~C) 2. A -> (D -> E) 3. ~(~B v ~D)      Log On


   

Question 196020: I need help finishing this proof.
A v (~B v ~C), A -> (D -> E), ~(~B v ~D) :. C -> (D -> E)
1. A v (~B v ~C)
2. A -> (D -> E)
3. ~(~B v ~D)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.  A v (~B v ~C)
2.  A -> (D -> E) 
3.  ~(~B v ~D)            :. C -> (D -> E) 
--------------------------
4.  A v ~(~~B & ~~C)                    1    De Morgan's Law
5.  A v ~(B & C)                        4    Double Negation
6.  ~(B & C) v A                        5    Commutation
7.  (B & C) -> A                        6    Material Implication
8.  B -> (C -> A)                       7    Exportation
----
9. ~~B & ~~D                            3    De Morgan's Law
10. B & D                               9    Double Negation
11. B                                  10    Simplification
12. C -> A                           8,11    Modus Ponens
13. C -> (D -> E)                    12,2    Hypothetical Syllogism