document.write( "Question 1042390: (PvQ)&R
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Algebra.Com's Answer #657366 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "1. (PvQ)&R\r\n" );
document.write( "2. (R&P)>S\r\n" );
document.write( "3. (Q&R)>S\r\n" );
document.write( "             Therefore, S\r\n" );
document.write( "       | 4. ~S          Assumption for Indirect Proof\r\n" );
document.write( "       | 5. R&(PvQ)     1, Commutation  \r\n" );
document.write( "       | 6. R           5, Simplification\r\n" );
document.write( "       | 7. ~(Q&R)      3,4 Modus Tollens\r\n" );
document.write( "       | 8. ~Qv~R       7, DeMorgan's law  \r\n" );
document.write( "       | 9. ~Rv~Q       8, Commutation\r\n" );
document.write( "       |10. ~~R         6, Double negation\r\n" );
document.write( "       |11. ~Q          9,10 Disjunctive syllogism \r\n" );
document.write( "       |12. PvQ         1, Simplification\r\n" );
document.write( "       |13. QvP         12, Commutation  \r\n" );
document.write( "       |14. P           13,11 Disjunctive syllogism\r\n" );
document.write( "       |15. R&P         6,14 Conjunction\r\n" );
document.write( "       |16. S           2,15 Modus ponens     \r\n" );
document.write( "       |17. S&~S        16,4 Conjunction   <--(contradiction)\r\n" );
document.write( "18. ~~S                 4-17 Indirect Proof\r\n" );
document.write( "19. S                   18, Double negation \r\n" );
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document.write( "Edwin

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