document.write( "Question 248098: I am working on proofs for my logic homework.\r
\n" ); document.write( "\n" ); document.write( "Here are the premises:\r
\n" ); document.write( "\n" ); document.write( "1. ~S -> (~G v ~F)
\n" ); document.write( "2. (~F -> ~W) & W\r
\n" ); document.write( "\n" ); document.write( "Here is the conclusion:\r
\n" ); document.write( "\n" ); document.write( "S v ~G \n" ); document.write( "
Algebra.Com's Answer #180839 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1.  ~S -> (~G v ~F)\r\n" );
document.write( "2.  (~F -> ~W) & W          / :. S v ~G\r\n" );
document.write( "----------------------------\r\n" );
document.write( "3.  ~~S v (~G v ~F)             1       Material Implication\r\n" );
document.write( "4.  S v (~G v ~F)               3       Double Negation\r\n" );
document.write( "5.  (S v ~G) v ~F               4       Association\r\n" );
document.write( "6.  ~F v (S v ~G)               5       Commutation\r\n" );
document.write( "7.  F -> (S v ~G)               6       Material Implication\r\n" );
document.write( "8.  W & (~F -> ~W)              2       Commutation\r\n" );
document.write( "9.  W                           8       Simplification\r\n" );
document.write( "10. ~~W                         9       Double Negation\r\n" );
document.write( "11. ~F -> ~W                    2       Simplification\r\n" );
document.write( "12. ~~F                         11,10   Modus Tollens\r\n" );
document.write( "13. F                           12      Double Negation\r\n" );
document.write( "14. S v ~G                      7,13    Modus Ponens\r\n" );
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