SOLUTION: Please help me solve this logic proof: 1. E→H 2. (E ∨ F) • (E ∨ G) 3. (F • G) → H conclusion is H

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Question 297185: Please help me solve this logic proof:
1. E→H
2. (E ∨ F) • (E ∨ G)
3. (F • G) → H conclusion is H

Answer by jim_thompson5910(35256)   (Show Source): You can 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
--------------------------------------
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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