document.write( "Question 1129426: construct a formal proof of validity for the following argument.
\n" ); document.write( "1. (M ⊃ N) ● (O ⊃ P)
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\n" ); document.write( "3. ~ (M ● O) ⊃ Q
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\n" ); document.write( "4. ∴ Q \n" ); document.write( "
Algebra.Com's Answer #746007 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. (M ⊃ N) ●(O ⊃ P) \r\n" );
document.write( "2. ~ N v ~ P \r\n" );
document.write( "3. ~ (M ● O) ⊃ Q     / ∴ Q\r\n" );
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document.write( "                     | 4.  ~Q                           AIP\r\n" );
document.write( "                     | 5.  ~~(M ● O)               3,MT\r\n" );
document.write( "                     | 6.  M ● O                   5,DN\r\n" );
document.write( "                     | 7.  M                       6,simp\r\n" );
document.write( "                     | 8.  O ● M                   6,commutation\r\n" );
document.write( "                     | 9.  O                       8,simp\r\n" );
document.write( "                     |10. M ⊃ N                    1,simp\r\n" );
document.write( "                     |11. N                        10,MP\r\n" );
document.write( "                     |12. (O ⊃ P) ● (M ⊃ N)        1,commutation \r\n" );
document.write( "                     |13. O ⊃ P                    12,simp\r\n" );
document.write( "                     |14. P                        13,9,MP\r\n" );
document.write( "                     |15. N ● P                    11,13,conjunction\r\n" );
document.write( "                     |16. ~(N ● P)                 2, deMorgan\r\n" );
document.write( "                     |17. (N ● P)● ~(N ● P)        15,16, conjunction\r\n" );
document.write( "18. Q       lines 4-17  Indirect Proof, (#17 is a contradiction)\r\n" );
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document.write( "Edwin

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