document.write( "Question 248179: This one is ridiculous, please help me with this proof.\r
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Algebra.Com's Answer #180938 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1.  (~B v A) -> (C & D)\r\n" );
document.write( "2.  A -> ~C\r\n" );
document.write( "3.  ~A -> ~B               /:.  ~(B <-> C)\r\n" );
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document.write( "4.  ~(~B v A) v (C & D)              1       Material Implication\r\n" );
document.write( "5.  (~~B & ~A) v (C & D)             4       De Morgan's Law\r\n" );
document.write( "6.  (B & ~A) v (C & D)               5       Double Negation\r\n" );
document.write( "7.  [(B & ~A) v C] & [(B & ~A) v D]  6       Distribution\r\n" );
document.write( "8.  [C v (B & ~A)] & [D v (B & ~A)]  7       Commutation\r\n" );
document.write( "9.  C v (B & ~A)                     8       Simplification\r\n" );
document.write( "10. (C v B) & (C v ~A)               9       Distribution\r\n" );
document.write( "11. C v B                            10      Simplification\r\n" );
document.write( "12. B v C                            11      Commutation\r\n" );
document.write( "13. ~~B v C                          12      Double Negation\r\n" );
document.write( "14. ~B -> C                          13      Material Implication\r\n" );
document.write( "15. B -> A                           3       Transposition\r\n" );
document.write( "16. B -> ~C                          15,2    Hypothetical Syllogism\r\n" );
document.write( "17. (B -> ~C) & (~B -> C)            16,14   Conjunction\r\n" );
document.write( "18. (~B v ~C) & (~~B v C)            17      Material Implication\r\n" );
document.write( "19. (~B v ~C) & (~~B v ~~C)          18      Double Negation\r\n" );
document.write( "20. ~(B & C) & ~(~B & ~C)            19      De Morgan's Law\r\n" );
document.write( "21. ~[(B & C) v (~B & ~C)]           20      De Morgan's Law\r\n" );
document.write( "22. ~(B <-> C)                       21      Material Equivalence\r\n" );
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