Question 388751: ~Bv[(C>D)•(E>D)]
B•(CvE)
Conclusion: D
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
1. ~B v [ (C -> D) * (E -> D)]
2. B * (C v E) /:. D
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3. (C v E) * B 2 Commutation
4. B 2 Simplification
5. C v E 3 Simplification
6. E v C 5 Commutation
7. ~~E v C 6 Double Negation
8. ~E -> C 7 Material Implication
9. (C -> D) * (E -> D) 1,4 Modus Ponens
10. (E -> D) * (C -> D) 9 Commutation
11. C -> D 9 Simplification
12. E -> D 10 Simplification
13. ~D -> ~E 12 Transposition
14. ~E -> D 8,11 Hypothetical Syllogism
15. ~D -> D 13,14 Hypothetical Syllogism
16. ~~D v D 15 Material Implication
17. D v D 16 Double Negation
18. D 17 Tautology
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Jim
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