document.write( "Question 1164105: Logic: Set and operations - Cardinal numbers and surveys
\n" ); document.write( "A nurse conducted a survey with 75 patients admitted to the hospital.
\n" ); document.write( "Let B = (Blood) the set of patients with high Blood pressure,
\n" ); document.write( "C = (Cholesterol) the set of patients with high Cholesterol level,
\n" ); document.write( "S = (Smoke) the set of patients who Smoke cigarettes.\r
\n" ); document.write( "\n" ); document.write( "The information from the nurse is as follows:
\n" ); document.write( "n(B)=47; n(B∩S)=33; n(C)=46; n(B∩C)=31; n(S)=52; n(B∩C∩S)=21;
\n" ); document.write( "n[(B∩C)∪(B∩S)∪(C∩S)]=51.\r
\n" ); document.write( "\n" ); document.write( "Find the number of patients who
\n" ); document.write( "(a) had high blood pressure or high cholesterol, but not both?
\n" ); document.write( "(b) had fewer than two of the conditions listed?
\n" ); document.write( "(c) were smokers, but did not have high blood pressure or high cholesterol?
\n" ); document.write( "(d) did not present exactly two of the conditions on the list? \n" ); document.write( "
Algebra.Com's Answer #788480 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Begin with n(B∩C∩S)=g=21\r\n" );
document.write( "Then go to n(B∩S)=f+g=33, and you can get f.\r\n" );
document.write( "Then go to n(B∩C)=d+g=31, and you can get d.\r\n" );
document.write( "Then go to n(B)=a+d+f+g=47, and you can get a.\r\n" );
document.write( "Then go to n[(B∩C)∪(B∩S)∪(C∩S)]=d+g+f+h=51, and you can get h.\r\n" );
document.write( "Then go to n(C)=d+e+g+h=46, and you can get e.\r\n" );
document.write( "Then go to n(S)=f+g+h+i=52, and you can get i.\r\n" );
document.write( "Finally, go to \"75 patients\", a+d+e+f+g+h+i+j=75, and you can get j.\r\n" );
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document.write( "(a) had high blood pressure or high cholesterol, but not both? \r\n" );
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document.write( "That's a+f+e+h.\r\n" );
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document.write( "(b) had fewer than two of the conditions listed?\r\n" );
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document.write( "That's a+e+i+j.\r\n" );
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document.write( "(c) were smokers, but did not have high blood pressure or high cholesterol?\r\n" );
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document.write( "That's i.\r\n" );
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document.write( "(d) did not present exactly two of the conditions on the list?\r\n" );
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document.write( "That's a+e+i+g+j\r\n" );
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document.write( "You can fill in the question marks in the Venn diagram, then add\r\n" );
document.write( "them up to answer the questions.\r\n" );
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document.write( "Edwin
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