document.write( "Question 971097: A -> (B & C)
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\n" ); document.write( "~(D -> I) / therefore, (A & G) -> (~I & ~E) \n" ); document.write( "
Algebra.Com's Answer #593776 by Edwin McCravy(20055)\"\" \"About 
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document.write( " 1.  A -> (B & C)\r\n" );
document.write( " 2.  C -> (E -> I)\r\n" );
document.write( " 3.  ~(D -> I)	\r\n" );
document.write( "        / therefore, (A & G) -> (~I & ~E)\r\n" );
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document.write( " 4. (A -> B) & (A -> C)          1, composition\r\n" );
document.write( " 5. A -> C                       4, simplification\r\n" );
document.write( " 6. A -> (E -> I)              2,5, hypothetical syllogism\r\n" );
document.write( " 7. (A & E) -> I                 6, exportation\r\n" );
document.write( " 8. ~I -> ~(A & E)               7, contrapositive\r\n" );
document.write( " 9. ~(~D v I)                    3, material implication\r\n" );
document.write( "10. ~~D & ~I                     9, DeMorgan's law\r\n" );
document.write( "11. D & ~I                      10, double negation\r\n" );
document.write( "12. ~I                          11, simplification\r\n" );
document.write( "13. ~(A & E)                  8,12, hypothetical syllogism       \r\n" );
document.write( "14. ~A v ~E                     13, DeMorgan's law\r\n" );
document.write( "15. A -> ~E                     14, material implication\r\n" );
document.write( "16. (A -> ~E) v ~G              15, addition\r\n" );
document.write( "17. (~A v ~E) v ~G              16, material implication \r\n" );
document.write( "18. ~A v (~E v ~G)              17, association\r\n" );
document.write( "19. ~A v (~G v ~E)              18, commutation\r\n" );
document.write( "20. (~A v ~G) v ~E              19, association\r\n" );
document.write( "21. ~(A & G) v ~E               20, DeMorgan's law\r\n" );
document.write( "22. (A & G) -> ~E               21, exportation\r\n" );
document.write( "23. ~E -> ~E & ~I               12, natural deduction\r\n" );
document.write( "24. (A & G) -> (~E & ~I)     22,23, hypothetical syllogism\r\n" );
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document.write( "Edwin
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