document.write( "Question 1206425: Premise:
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\n" ); document.write( "\n" ); document.write( "Use either indirect proof or conditional proof (or both) and the eighteen rules of inference to derive the conclusion of the following symbolized argument. \n" ); document.write( "
Algebra.Com's Answer #843934 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I am not sure what symbol you use for conjunction (AND), maybe a dot,\r\n" );
document.write( "but I will use &.\r\n" );
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document.write( "Premise:\r\n" );
document.write( "1. F\r\n" );
document.write( "Conclusion:\r\n" );
document.write( "(G ⊃ H) ∨ (~G ⊃ J)\r\n" );
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document.write( "      | 2.  ~[(G ⊃ H) ∨ (~G ⊃ J)]      Assumption for Indirect Proof\r\n" );
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document.write( "      | 3.  ~(G ⊃ H) & ~(~G ⊃ J)       2, DeMorgan's Law\r\n" );
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document.write( "      | 4.  ~(~G V H) & ~(~~G ∨ J)      3, Material Implication (twice)         \r\n" );
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document.write( "      | 5.  ~(~G V H) & ~(G ∨ J)        4, Double Negation\r\n" );
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document.write( "      | 6. (~~G & ~H) & (~G & ~J)       5, DeMorgan's Law (twice)\r\n" );
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document.write( "      | 7. (G & ~H) & (~G & ~J)         6, Double Negation\r\n" );
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document.write( "      | 8. (G & ~H) & [~G & ~J]         7, Changing () to [] for clarity\r\n" );
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document.write( "      | 9. [(G & ~H) & ~G] & ~J         8, Association\r\n" );
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document.write( "      |10. [G & (~H & ~G)] & ~J         9, Association\r\n" );
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document.write( "      |11. [G & (~G & ~H)] & ~J        10, Commutation\r\n" );
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document.write( "      |12. [(G & ~G) & ~H] & ~J        11, Association         \r\n" );
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document.write( "      |13. (G & ~G) & [~H & ~J]        12, Association\r\n" );
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document.write( "      |14. G & ~G                      13, Simplification\r\n" );
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document.write( "15. F     lines 2-14 for Indirect Proof\r\n" );
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document.write( "Comment: This is a case where the conclusion is a tautology, and since a\r\n" );
document.write( "tautology is always true, then the conclusion is always true. So regardless\r\n" );
document.write( "of what we are given as premises (in this case only F), the conclusion will\r\n" );
document.write( "always be true. \r\n" );
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document.write( "Edwin
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