SOLUTION: 1. A -> ~(B v C) 2. ~D -> (~A -> ~E) 3. ~(~E v F) 4. ~F -> (A -> B) /D I don't understand how to do this proof with the conclusion being "D".

Algebra ->  Proofs -> SOLUTION: 1. A -> ~(B v C) 2. ~D -> (~A -> ~E) 3. ~(~E v F) 4. ~F -> (A -> B) /D I don't understand how to do this proof with the conclusion being "D".      Log On


   

Question 1026581: 1. A -> ~(B v C)
2. ~D -> (~A -> ~E)
3. ~(~E v F)
4. ~F -> (A -> B) /D
I don't understand how to do this proof with the
conclusion being "D".
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
I won't waste time with trivial 'double negation' 
and 'commutation'.

1. A -> ~(BvC)
2. ~D -> (~A->~E)
3. ~(~EvF)
4. ~F->(A->B)   	/D 

5. ~(~A->~E)->D       2, Transposition
6. ~(Av~E)->D         5, Material Implication
7. (~A&E)->D          6, DeMorgan's Law
8. E&~F               3, DeMorgan's law
9. ~F                 8, Simplification
10. A->B              4,9, Modus ponens
11. A->(~B&~C)        1, DeMorgan's law
12. A->~B             11, Simplification
13. (A->B)&(A->~B)    10,12, Conjunction of premises
14. ~A                13, Negative introduction
15. E                 8, Simplification
16. ~A&E              14,15, Conjunction of premises
17. D                 7,16, Modus ponens    

Edwin