document.write( "Question 249372: I need to solve this conditional proof and I can't. Help?\r
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Algebra.Com's Answer #181645 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: With conditional proofs, we assume the antecedent of the conclusion. In this case, we're assuming ~L which we'll denote with C.P (for conditional proof). Also, I'm going to use '&' in place of '.'\r
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document.write( "1.  ~(M & ~L) -> Q          / :. ~L -> Q\r\n" );
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document.write( "2.  ~L                                  C.P.\r\n" );
document.write( "3.  ~~(M & ~L) v Q             1        Material Implication\r\n" );
document.write( "4.  (M & ~L) v Q               3        Double Negation\r\n" );
document.write( "5.  Q v (M & ~L)               4        Commutation\r\n" );
document.write( "6.  (Q v M) & (Q v ~L)         5        Distribution\r\n" );
document.write( "7.  (Q v ~L) & (Q v M)         6        Commutation\r\n" );
document.write( "8.  Q v ~L                     7        Simplification\r\n" );
document.write( "9.  ~~Q v ~L                   8        Double Negation\r\n" );
document.write( "10. ~Q -> ~L                   9        Material Implication\r\n" );
document.write( "11. ~L v ~L                    2        Addition\r\n" );
document.write( "12. ~~L v ~L                   11       Double Negation\r\n" );
document.write( "13. L -> ~L                    12       Material Implication\r\n" );
document.write( "14. ~L -> ~~L                  13       Transposition\r\n" );
document.write( "15. ~L -> L                    14       Double Negation\r\n" );
document.write( "16. ~Q -> L                    10,15    Hypothetical Syllogism\r\n" );
document.write( "17. ~L -> ~~Q                  16       Transposition\r\n" );
document.write( "18. ~L -> Q                    17       Double Negation\r\n" );
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