document.write( "Question 996678: I'm having a really hard time with the following proof:
\n" ); document.write( "A&B, AvC :. (A->B) & (C->A)\r
\n" ); document.write( "\n" ); document.write( "My prof has warned us that the second premise, AvC, is a distraction, but I don't really understand how to do this then. \n" ); document.write( "
Algebra.Com's Answer #616713 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. A&B \r\n" );
document.write( "2. AvC  \r\n" );
document.write( "              :. (A->B) & (C->A)\r\n" );
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document.write( "Your prof is wrong.  This argument is not valid.\r\n" );
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document.write( "Here is the counter-example:\r\n" );
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document.write( "Suppose that A is false, B is true, and C is false.\r\n" );
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document.write( "Then A&B is false, AvC is false, therefore the\r\n" );
document.write( "conjunction of the premises (A&B)&(AvC) is false.\r\n" );
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document.write( "Now let's look at the conclusion:\r\n" );
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document.write( "A->B is true, C->A is true, therefore (A->B) & (C->A) is true.\r\n" );
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document.write( "So this is a case where the conjunction of premises is false\r\n" );
document.write( "and the conclusion is true.\r\n" );
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document.write( "So the argument is invalid.  Be sure to tell your prof why.\r\n" );
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document.write( "Edwin

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