document.write( "Question 1198251: 1.S>(R&~T)
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\n" ); document.write( "3.(Qv~T)>~E /~S \n" ); document.write( "

Algebra.Com's Answer #831837 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "1.S>(R&~T)\r\n" );
document.write( "2.(S&R)>(TvE)\r\n" );
document.write( "3.(Qv~T)>~E      /~S\r\n" );
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document.write( "              |4.  ~~S       Assumption for indirect proof\r\n" );
document.write( "              |5.  S         4, double negation\r\n" );
document.write( "              |6.  R&~T      1,5, modus ponens\r\n" );
document.write( "              |7.  R         6, simplification\r\n" );
document.write( "              |8.  ~T&R      6, commutativity\r\n" );
document.write( "              |9.  ~T        8, simplification\r\n" );
document.write( "              |10.  S&R      5,6, conjunction\r\n" );
document.write( "              |11.  TvE      2,10, modus ponens   \r\n" );
document.write( "              |12.  E        11,9, disjunctive syllogism\r\n" );
document.write( "              |13.  ~~E      12, double negation\r\n" );
document.write( "              |14.  ~(Qv~T)  3,13 modus tollens \r\n" );
document.write( "              |15.  ~Q&~~T   14, deMorgan's law\r\n" );
document.write( "              |16.  ~Q&T     15, double negation\r\n" );
document.write( "              |17.  T&~Q     16, commutation\r\n" );
document.write( "              |18.  T        17, simplification\r\n" );
document.write( "              |19.  T&~T     18,9, conjunction\r\n" );
document.write( "20.  ~S       lines 4-19  indirect proof\r\n" );
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document.write( "Edwin

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