SOLUTION: A -> D ~C -> ~D (C v D) -> ~C / therefore, A -> E

Question 971096: A -> D
~C -> ~D
(C v D) -> ~C / therefore, A -> E
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

 1. A -> D
 2. ~C -> ~D
 3. (C v D) -> ~C	/ therefore, A -> E

 4. ~~D -> ~~C               2, contrapositive
 5. D -> C                   4, double negation 
 6. ~~C -> ~(C v D)          3, contrapositive
 7. C -> ~(C v D)            6, double negation
 8. C -> (~C & ~D)           7, DeMorgan's law
 9. (C -> ~C) & (C -> ~D)    8, composition
10. C -> ~C                  9, simplification
11. ~C v ~C                 10, material implication
12. ~C                      11, simplification
13. ~C v E                  12, addition
14.  A -> C                1,5, hypothetical syllogism
15.  C -> E                 13, material implication
16.  A -> E              14,15, hypothetical syllogism   

Edwin

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