document.write( "Question 296755: I have tried this several ways and cant' get it .\r
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\n" ); document.write( "4.G->(EvL) :. (G*~L)->K \n" ); document.write( "

Algebra.Com's Answer #213787 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
The idea with these derivations is to include all of the given premises. It helps to fully know the 19 rules of inference (preferably by heart) so you might be able to recognize the answer easier. \r
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document.write( "1.  (G * P) -> K\r\n" );
document.write( "2.  E -> Z\r\n" );
document.write( "3.  ~P -> ~Z\r\n" );
document.write( "4.  G ->(E v L)  :. (G * ~L) -> K\r\n" );
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document.write( "5.  ~~Z -> ~~P                             3         Transposition\r\n" );
document.write( "6.  Z -> P                                 5         Double Negation\r\n" );
document.write( "7.  E -> P                                 2,6       Hypothetical Syllogism\r\n" );
document.write( "8.  (P * G) -> K                           1         Commutation\r\n" );
document.write( "9.  P -> (G -> K)                          8         Exportation\r\n" );
document.write( "10. E -> (G -> K)                          7,9       Hypothetical Syllogism\r\n" );
document.write( "11. ~G v (E v L)                           4         Material Implication\r\n" );
document.write( "12. (~G v E) v L                           11        Association\r\n" );
document.write( "13. (E v ~G) v L                           12        Commutation\r\n" );
document.write( "14. (~~E v ~G) v L                         13        Double Negation\r\n" );
document.write( "15. ~(~E * G) v L                          14        De Morgan's Law\r\n" );
document.write( "16. (~E * G) -> L                          15        Material Implication\r\n" );
document.write( "17. ~E -> (G -> L)                         16        Exportation\r\n" );
document.write( "18. ~(G -> L) -> ~~E                       17        Transposition\r\n" );
document.write( "19. ~(G -> L) -> E                         18        Double Negation\r\n" );
document.write( "20. ~(G -> L) -> (G -> K)                  19,10     Hypothetical Syllogism\r\n" );
document.write( "21. (G -> L) v (G -> K)                    20        Material Implication\r\n" );
document.write( "22. (~G v L) v (~G v K)                    21        Material Implication\r\n" );
document.write( "23. ~G v (L v ~G) v K                      22        Association\r\n" );
document.write( "24. ~G v (~G v L) v K                      23        Commutation\r\n" );
document.write( "25. (~G v ~G) v (L v K)                    24        Association\r\n" );
document.write( "26. ~G v (L v K)                           25        Tautology\r\n" );
document.write( "27. (~G v L) v K                           26        Association\r\n" );
document.write( "28. (~G v ~~L) v K                         27        Double Negation\r\n" );
document.write( "29. ~(G * ~L) v K                          28        De Morgan's Law\r\n" );
document.write( "30. (G * ~L) -> K                          29        Material Implication\r\n" );
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