document.write( "Question 114116: How would this be translated?
\n" ); document.write( "Tulane increasing enrollment is a necessary condition for Duke’s reducing class size if and only if Fordham’s raising tuition is a sufficient condition for Georgetown’s expanding course offerings. \r
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Algebra.Com's Answer #83133 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
How would this be translated?
\n" ); document.write( "Tulane increasing enrollment is a necessary condition for Duke’s reducing class size if and only if Fordham’s raising tuition is a sufficient condition for Georgetown’s expanding course offerings\r
\n" ); document.write( "\n" ); document.write( "How would this be translated?
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document.write( "Let \r\n" );
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document.write( "p = \"Tulane increases enrollment\"\r\n" );
document.write( "q = \"Duke’s reduces class size\"\r\n" );
document.write( "r = \"Fordham’s raises tuition\"\r\n" );
document.write( "s = \"Georgetown expands course offerings\"\r\n" );
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document.write( "Then the original statement becomes:\r\n" );
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document.write( "p is a necessary condition for q if and only if \r\n" );
document.write( "r is a sufficient condition for s.\r\n" );
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document.write( "Put in parentheses around the parts:\r\n" );
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document.write( "(p is a necessary condition for q) if and only if\r\n" );
document.write( "(r is a sufficient condition for s)\r\n" );
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document.write( "Now use these rules\r\n" );
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document.write( "X is a necessary condition for Y ------ Y ® X \r\n" );
document.write( "X if and only if Y -------------------- X « Y \r\n" );
document.write( "X is a sufficient condition for Y ----- X ®            \r\n" );
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document.write( "(p is a necessary condition for q) if and only if \r\n" );
document.write( "(r is a sufficient condition for s)\r\n" );
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document.write( "(q ® p) « (r ® s)            \r\n" );
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document.write( "That's the final translation.\r\n" );
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document.write( "Note: \r\n" );
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document.write( "A sufficient condition always goes on the LEFT of ® \r\n" );
document.write( "A necessary condition always goes on the RIGHT of ®\r\n" );
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document.write( "SUFFICIENT ® NECESSARY\r\n" );
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document.write( "Edwin
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