document.write( "Question 1199145: Use one of the 3 methods of syllogistic logic to determine whether the following syllogism is
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\n" ); document.write( "No carrots are red fruits.
\n" ); document.write( "Some fruits are carrots.
\n" ); document.write( "Therefore, some fruits are not red fruits. \n" ); document.write( "
Algebra.Com's Answer #832960 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Use one of the 3 methods of syllogistic logic to determine whether the following syllogism is
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\n" ); document.write( "No carrots are red fruits.
[Translation: if we have something that fits the category of being a carrot, then\r\n" );
document.write( "it does not fit both the category of being red and the category of being a fruit.]\r\n" );
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document.write( "C ⊃ ~(R • F)
Some fruits are carrots.
[Translation: We DO have some things that fit the category of being a fruit and\r\n" );
document.write( "the category of being a carrot.\r\n" );
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document.write( "F • C
Therefore, some fruits are not red fruits.
[Translation: We DO have some things that fit the category of being a fruit but (and) \r\n" );
document.write( "do not fit the category of being red.]\r\n" );
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document.write( "F • ~R\r\n" );
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document.write( "1.  C ⊃ ~(R • F)\r\n" );
document.write( "2.  F • C                 / F  • ~R\r\n" );
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document.write( "3.  F        2, simplification\r\n" );
document.write( "4.  C • F    2, commutation\r\n" );
document.write( "5.  C        4, simplification\r\n" );
document.write( "6.  ~(R • F) 1,5 modus ponens\r\n" );
document.write( "7.  ~R v ~F  6, DeMorgan's law \r\n" );
document.write( "8.  ~F v ~R  7, commutation\r\n" );
document.write( "9.  ~~F      3, double negation\r\n" );
document.write( "10. ~R       8,9, disjunctive syllogism\r\n" );
document.write( "11. F • ~R   3,10 conjunction\r\n" );
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document.write( "The conclusion has been reached. This shows that the argument is valid.\r\n" );
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document.write( "Edwin
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