document.write( "Question 293878: Use an ordinary proof to solve
\n" ); document.write( "1) 1.E ⊃ (S ⊃ T)
\n" ); document.write( " 2.(~L ⋅ M)⊃(S ⋅ E)
\n" ); document.write( " 3.~ (T v L) /~M \n" ); document.write( "
Algebra.Com's Answer #525303 by jim_thompson5910(35256)\"\" \"About 
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document.write( "1.  E -> (S -> T)\r\n" );
document.write( "2.  (~L & M) -> (S & E)\r\n" );
document.write( "3.  ~(T v L) \r\n" );
document.write( "Therefore, ~M\r\n" );
document.write( "-------------------------------------------------------\r\n" );
document.write( "4.  (E & S) -> T                         1         Exp\r\n" );
document.write( "5.  (~L & M) -> T                        2,4       HS\r\n" );
document.write( "6.  ~T & ~L                              3         DM\r\n" );
document.write( "7.  ~L & ~T                              6         Comm\r\n" );
document.write( "8.  ~T                                   6         Simp\r\n" );
document.write( "9.  ~L                                   7         Simp\r\n" );
document.write( "10. ~(~L & M)                            5,8       MT\r\n" );
document.write( "11. ~~L v ~M                             10        DM\r\n" );
document.write( "12. ~M                                   11,9      DS\r\n" );
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\n" ); document.write( "\n" ); document.write( "Abbreviations/Acronyms Used:\r
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\n" ); document.write( "\n" ); document.write( "Comm = Commutation
\n" ); document.write( "DM = De Morgan's Law
\n" ); document.write( "DS = Disjunctive Syllogism
\n" ); document.write( "Exp = Exportation
\n" ); document.write( "HS = Hypothetical Syllogism
\n" ); document.write( "MT = Modus Tollens
\n" ); document.write( "Simp = Simplification \n" ); document.write( "
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