document.write( "Question 1188875: Use conditional proof or indirect proof as needed:
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Algebra.Com's Answer #820618 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You don't need all those x's and (x)'s.   They just get in\r\n" );
document.write( "the way. And we know they're understood.\r\n" );
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document.write( "Use conditional proof or indirect proof as needed:\r\n" );
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document.write( "1. R ⊃ (T • ∼E)	 \r\n" );
document.write( "2. (Q • R) ⊃ E	   / R ⊃ ∼Q\r\n" );
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document.write( "3.             | R        Assumption for Conditional proof\r\n" );
document.write( "4.             | T • ∼E   1,3, Modus Ponens\r\n" );
document.write( "5.             |~E • T    4, Commutation\r\n" );
document.write( "6.             |~E        5, Simplification\r\n" );
document.write( "7.             |~(Q • R)  2,6,  Modus tollens\r\n" );
document.write( "8.             |~Q ∨ ~R   7, DeMordan's law\r\n" );
document.write( "9.             |~R ∨ ~Q   8, Commutation\r\n" );
document.write( "10.            |~~R       3, Double negation\r\n" );
document.write( "11.            |~Q        9,10, Disjunctive syllogism\r\n" );
document.write( "12. R ⊃ ∼Q    lines 3-11  Conditional proof\r\n" );
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document.write( "Edwin

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