document.write( "Question 1038513: Solve the problem using rules of inference and replacement:\r
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Algebra.Com's Answer #653490 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "    1:   Q or (R and S)\r\n" );
document.write( "    2:   (Q -> T) and (T -> S)    |    S\r\n" );
document.write( "    3:   Assume Q\r\n" );
document.write( "         4:  Q -> T               2    Conjunction Elimination\r\n" );
document.write( "         5:  T                    3,4  Modus Ponens\r\n" );
document.write( "         6:  T -> S               2    Conjunction Elimination\r\n" );
document.write( "         7:  S                    5,6  Modus Ponens\r\n" );
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document.write( "    8:   Assume ~Q\r\n" );
document.write( "         9:  R and S              1,8  Disjunctive Syllogism\r\n" );
document.write( "        10:  S                    9    Conjunction Elimination\r\n" );
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document.write( "   11:   :. S                     3-7,8-10 Law of Excluded Middle\r\n" );
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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