document.write( "Question 1179695: INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem.\r
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\n" ); document.write( "1. M ⊃ (∼B ⊃ J)
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Algebra.Com's Answer #838337 by RBryant(14)\"\" \"About 
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document.write( "Here is a proof using the Introduction and Elimination Rules of Natural Deduction:\r\n" );
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document.write( "1. M ⊃ (∼B ⊃ J)	 \r\n" );
document.write( "2. B ⊃ (~M * ~M)	 \r\n" );
document.write( "3. ∼J	/ ∴  ~M \r\n" );
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document.write( "4.      M            Assumption\r\n" );
document.write( "5.      ~B ⊃ J       1,4                 ⊃E\r\n" );
document.write( "6.           B            Assumption      \r\n" );
document.write( "7.      ~M & ~M       2,6                 &I\r\n" );
document.write( "8.      ~M            7                   &E\r\n" );
document.write( "9.      M & ~M        4,8                 &I\r\n" );
document.write( "10.      ~B           6-9                 ~I\r\n" );
document.write( "11.     B & ~B        6,10                &I\r\n" );
document.write( "12. ~M                4-11                ~I\r\n" );
document.write( "                                                 QED\r\n" );
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document.write( "HERE is a Proof using Copi Rules:\r\n" );
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document.write( "1. M ⊃ (∼B ⊃ J)	 \r\n" );
document.write( "2. B ⊃ (~M * ~M)	 \r\n" );
document.write( "3. ∼J	/ ∴  ~M \r\n" );
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document.write( "4. B ⊃ (~M & ~M)                    2      Tautology\r\n" );
document.write( "5. ~(~B ⊃ J) ⊃ ~M                   4      Transposition\r\n" );
document.write( "6. (~B ⊃ J) v ~M                    5       Material Implication\r\n" );
document.write( "7. ~ ~B v J v ~M                     6      Material Implication\r\n" );
document.write( "8. B v J v ~M                        7      Double Negation\r\n" );
document.write( "9. (B v ~M) v J                      8      Association\r\n" );
document.write( "10. B v ~M                           9      Disjunctive Syllogism\r\n" );
document.write( "11. ~B ⊃ ~M                         10      Material Implication                           \r\n" );
document.write( "12. M ⊃ B                           11      Transposition\r\n" );
document.write( "13. M ⊃ ~M                          4,12    Hypothetical Syllogism\r\n" );
document.write( "14. ~M v ~M                          13      Material Implication\r\n" );
document.write( "15. ~M                               14      Tautology\r\n" );
document.write( "                                                                     QED\r\n" );
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