document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119159>Question 1119159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 100 students, the numbers taking various courses were found to be English, 59; mathematics, 44; chemistry, 48; English and mathematics, 24; English and chemistry, 26; mathematics and chemistry, 31; and courses in all three areas, 16.\r<BR>\n" );
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document.write( "(a) How many students were taking mathematics, but neither English nor chemistry?\r<BR>\n" );
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document.write( "(b) How many were taking mathematics and chemistry, but not English?\r<BR>\n" );
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document.write( "(c) How many were taking English and chemistry, but not mathematics?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734633 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "In a survey of 100 students, the numbers taking various courses were found to be <BR>\n" );
document.write( "English, 59; mathematics, 44; chemistry, 48; English and mathematics, 24; English and chemistry, 26; mathematics and chemistry, 31; <BR>\n" );
document.write( "and courses in all three areas, 16.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  How many students were taking mathematics, but neither English nor chemistry?\r\n" );
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document.write( "     M - EM - MC + EMC = 44 - 24 - 31 + 16 = 5.\r\n" );
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document.write( "(b)  How many were taking mathematics and chemistry, but not English?\r\n" );
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document.write( "     MC - EMC = 31 - 16 = 15.\r\n" );
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document.write( "(c)  How many were taking English and chemistry, but not mathematics?\r\n" );
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document.write( "     EC - EMC = 26 - 16 = 10.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "In this solution, two-letter abbreviation means intersection of two sub-sets.\r<BR>\n" );
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