document.write( "Question 250587: 1) Vv(F&G)
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Algebra.Com's Answer #182499 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: I'm going to use ~ for the negation symbol\r
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document.write( "1)  V v (F & G)\r\n" );
document.write( "2)  V -> E\r\n" );
document.write( "3)  G -> (M -> I)\r\n" );
document.write( "4)  M                  // therefore, I v E\r\n" );
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document.write( "5)  (V v F) & (V v G)                     1       Distribution\r\n" );
document.write( "6)  (V v G) & (V v F)                     5       Commutation\r\n" );
document.write( "7)  V v G                                 6       Simplification\r\n" );
document.write( "8)  ~~V v G                               7       Double Negation\r\n" );
document.write( "9)  ~V -> G                               8       Material Implication\r\n" );
document.write( "10) ~G -> ~~V                             9       Transposition\r\n" );
document.write( "11) ~G -> V                              10       Double Negation\r\n" );
document.write( "12) ~G -> E                              11,2     Hypothetical Syllogism\r\n" );
document.write( "13) ~E -> ~~G                            12       Transposition\r\n" );
document.write( "14) ~E -> G                              13       Double Negation\r\n" );
document.write( "15) ~E -> (M -> I)                       14,3     Hypothetical Syllogism    \r\n" );
document.write( "16) (~E & M) -> I                        15       Exportation\r\n" );
document.write( "17) (M & ~E) -> I                        16       Commutation\r\n" );
document.write( "18) M -> (~E -> I)                       17       Exportation\r\n" );
document.write( "19) M -> (~~E v I)                       18       Material Implication\r\n" );
document.write( "20) M -> (E v I)                         19       Double Negation\r\n" );
document.write( "21) E v I                                20,4     Modus Ponens\r\n" );
document.write( "22) I v E                                21       Commutation\r\n" );
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