document.write( "Question 870562: 1.M<->N
\n" ); document.write( "2.~Mv~N
\n" ); document.write( "3.O>M
\n" ); document.write( "/~(NvO) \n" ); document.write( "

Algebra.Com's Answer #524944 by jim_thompson5910(35256) $\"\"$ $\"About$

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document.write( "1.  M <-> N\r\n" );
document.write( "2.  ~M v ~N\r\n" );
document.write( "3.  O -> M\r\n" );
document.write( "/~(N v O)\r\n" );
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document.write( "4.  (M -> N) & (N -> M)                    1        ME\r\n" );
document.write( "5.  (N -> M) & (M -> N)                    4        Comm\r\n" );
document.write( "6.  N -> M                                 5        Simp\r\n" );
document.write( "7.  ~~M -> ~N                              2        MI\r\n" );
document.write( "8.  M -> ~N                                7        DN\r\n" );
document.write( "9.  N -> ~N                                6,8      HS\r\n" );
document.write( "10. ~~N -> ~N                              9        DN\r\n" );
document.write( "11. ~N v ~N                                10       MI\r\n" );
document.write( "12. ~N                                     11       Taut\r\n" );
document.write( "13. M -> N                                 4        Simp\r\n" );
document.write( "14. M -> ~~N                               13       DN\r\n" );
document.write( "15. ~M                                     14,12    MT\r\n" );
document.write( "16. O -> ~~M                               3        DN\r\n" );
document.write( "17. ~O                                     16,15    MT\r\n" );
document.write( "18. ~N & ~O                                12,17    Conj\r\n" );
document.write( "19. ~(~~N v ~~O)                           18       DM\r\n" );
document.write( "20. ~(N v O)                               19       DN\r\n" );
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\n" ); document.write( "\n" ); document.write( "Abbreviations/Acronyms Used:\r
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\n" ); document.write( "\n" ); document.write( "Comm = Commutation
\n" ); document.write( "Simp = Simplification
\n" ); document.write( "MT = Modus Tollens
\n" ); document.write( "Taut = Tautology
\n" ); document.write( "Conj = Conjunction
\n" ); document.write( "DN = Double Negation
\n" ); document.write( "ME = Material Equivalence
\n" ); document.write( "MI = Material Implication
\n" ); document.write( "HS = Hypothetical Syllogism
\n" ); document.write( "DM = De Morgan's Law \n" ); document.write( "

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