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put this solution on YOUR website! With these derivations, it helps to know the 19 rules of inference.
1. E -> H
2. (E v F) * (E v G)
3. (F * G) -> H :. H
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4. E v F 2 Simplification
5. F v E 4 Commutation
6. ~~F v E 5 Double Negation
7. ~F -> E 6 Material Implication
8. ~F -> H 7,1 Hypothetical Syllogism
9. (E v G) * (E v F) 2 Commutation
10. E v G 9 Simplification
11. ~~E v G 10 Double Negation
12. ~E -> G 11 Material Implication
13. ~G -> ~~E 12 Transposition
14. ~G -> E 13 Double Negation
15. ~G -> H 14,1 Hypothetical Syllogism
16. F -> (G -> H) 3 Exportation
17. F -> (~H -> ~G) 16 Transposition
18. (F * ~H) -> ~G 17 Exportation
19. (F * ~H) -> H 18,15 Hypothetical Syllogism
20. F -> (~H -> H) 19 Exportation
21. F -> (~~H v H) 20 Material Implication
22. F -> (H v H) 21 Double Negation
23. F -> H 22 Tautology
24. ~H -> ~F 23 Transposition
25. ~H -> H 24,8 Hypothetical Syllogism
26. ~~H v H 25 Material Implication
27. H v H 26 Double Negation
28. H 27 Tautology
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