document.write( "Question 1179971: Use an ordinary proof (not conditional or indirect) to solve the following arguments\r
\n" ); document.write( "\n" ); document.write( "1. P ⊃ ~M
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Algebra.Com's Answer #810420 by Edwin McCravy(20055)\"\" \"About 
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document.write( "1. P ⊃ ~M\r\n" );
document.write( "2. C ⊃ M\r\n" );
document.write( "3. ~L v C\r\n" );
document.write( "4. (~P ⊃ ~E) • (~E ⊃ ~C)\r\n" );
document.write( "5. P v ~P                     /~L\r\n" );
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document.write( " 6. ~P ⊃ ~E                 4, simplification\r\n" );
document.write( " 7. ~~E ⊃ ~~P               6, transposition\r\n" );
document.write( " 8. E ⊃ P                   7, double negation\r\n" );
document.write( " 9. E ⊃ ~M                  8,1 hypothetical syllogism\r\n" );
document.write( "10. ~E v ~M                 9, material implication\r\n" );
document.write( "11. ~(E • M)                10, deMorgan's law\r\n" );
document.write( "12. ~C v M                   2, material implication\r\n" );
document.write( "13. (~E ⊃ ~C) • (~P ⊃ ~E)   4, commutation\r\n" );
document.write( "14. ~E ⊃ ~C                 13, simplification\r\n" );
document.write( "15. ~~E v ~C                14, material implication\r\n" );
document.write( "16. E v ~C                  15, double negation\r\n" );
document.write( "17. ~C v E                  16, commutation\r\n" );
document.write( "18.  (~C v E) • (~C v M)    17,12, conjunction\r\n" );
document.write( "19. ~C v (E • M)            18, distribution\r\n" );
document.write( "20. (E • M) v ~C            19, commutation\r\n" );
document.write( "21. ~C                      20,11, disjunctive syllogism\r\n" );
document.write( "22. C v ~L                  3, commutation\r\n" );
document.write( "23. ~L                      22,21 disjunctive syllogism\r\n" );
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document.write( "Edwin
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