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

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

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Question 196027: I need help finishing this proof.
(A . B) -> (E -> A), (A . B) v C, C -> D :. (E -> A) v D
1. (A . B) -> (E -> A)
2. (A . B) v C
3. C -> D
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
1.  (A . B) -> (E -> A)
2.  (A . B) v C
3.  C -> D :. (E -> A) v D 
----------------------------------
4.  ~~(A . B) v C                   2       Double Negation
5.  ~(A . B) -> C                   4       Material Implication
6.  ~(A . B) -> D                 5,3       Hypothetical Syllogism
7.  ~D -> ~~(A . B)                 6       Transposition
8.  ~D -> (A . B)                   7       Double Negation
9.  ~D -> (E -> A)                8,1       Hypothetical Syllogism       
10. ~(E -> A) -> ~~D                9       Transposition
11. ~(E -> A) -> D                 10       Double Negation
12. (E -> A) v D                   11       Material Implication