document.write( "Question 189186: ~(A or B) or ~(C or D)\r
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Algebra.Com's Answer #141960 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: I'm going to use the symbol \"v\" for \"or\"\r
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document.write( "1. ~(A v B) v ~(C v D)\r\n" );
document.write( "2. (E v F) -> D   /     A -> ~E\r\n" );
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document.write( "3.  (~A & ~B) v (~C & ~D)                       1    De Morgan's Law\r\n" );
document.write( "4.  [(~A & ~B) v ~C] & [(~A & ~B) v ~D]         3    Distribution\r\n" );
document.write( "5.  [(~A & ~B) v ~D] & [(~A & ~B) v ~C]         4    Commutation\r\n" );
document.write( "6.  (~A & ~B) v ~D                              5    Simplification\r\n" );
document.write( "7.  ~D v (~A & ~B)                              6    Commutation\r\n" );
document.write( "8.  (~D v ~A) & (~D v ~B)                       7    Distribution\r\n" );
document.write( "9.  ~D v ~A                                     8    Simplification\r\n" );
document.write( "10. ~A v ~D                                     9    Commutation\r\n" );
document.write( "11. A -> ~D                                    10    Material Implication\r\n" );
document.write( "12. ~(E v F) v D                                2    Material Implication\r\n" );
document.write( "13. (~E & ~F) v D                              12    De Morgan's Law\r\n" );
document.write( "14. D v (~E & ~F)                              13    Commutation\r\n" );
document.write( "15. (D v ~E) & (D v ~F)                        14    Distribution\r\n" );
document.write( "16. D v ~E                                     15    Simplification\r\n" );
document.write( "17. ~~D v ~E                                   16    Double Negation\r\n" );
document.write( "18. ~D -> ~E                                   17    Material Implication\r\n" );
document.write( "19. A -> ~E                                 11,18    Hypothetical Syllogism\r\n" );
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