document.write( "Question 297185: Please help me solve this logic proof: \r
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Algebra.Com's Answer #214078 by jim_thompson5910(35256) $\"\"$ $\"About$

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