document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206848>Question 1206848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain class, 22 pupils take one or more of chemistry, economics and government.<BR>\n" );
document.write( "12 take economics (E), 8 take government (G) and 7 take chemistry (C). Nobody takes economics and chemistry and 4 pupils take economics and government.<BR>\n" );
document.write( "a) Draw a Venn diagram to illustrate the information.<BR>\n" );
document.write( "b) How many pupils take<BR>\n" );
document.write( "i) both chemistry and government?<BR>\n" );
document.write( "ii) government only?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844520 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=844520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "In a certain class, 22 pupils take one or more of chemistry, economics and government.<BR>\n" );
document.write( "12 take economics (E), 8 take government (G) and 7 take chemistry (C). <BR>\n" );
document.write( "Nobody takes economics and chemistry and 4 pupils take economics and government.<BR>\n" );
document.write( "a) Draw a Venn diagram to illustrate the information.<BR>\n" );
document.write( "b) How many pupils take<BR>\n" );
document.write( "i) both chemistry and government?<BR>\n" );
document.write( "ii) government only?<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( "We are given a Universal set (22 pupils) and 3 its basic subsets\r\n" );
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document.write( "    E  (12)\r\n" );
document.write( "    G   (8)\r\n" );
document.write( "    C   (7)\r\n" );
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document.write( "We also are given their in-pair intersections\r\n" );
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document.write( "    EC  (0, nobody)\r\n" );
document.write( "    EG  (4)\r\n" );
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document.write( "Let x be the number of pupils in the intersection CG.\r\n" );
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document.write( "We know that the triple intersection EGC is 0 (since EC is 0).\r\n" );
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document.write( "Write the inclusion-exclusion equality\r\n" );
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document.write( "    22 = 12 + 8 + 7 - 0 - 4 - x + 0,\r\n" );
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document.write( "or\r\n" );
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document.write( "    22 = 23 - x.\r\n" );
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document.write( "Hence,  x = 23 - 22 = 1.\r\n" );
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document.write( "So, the intersection CG is 1 pupil.  It is the answer to question (i).\r\n" );
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document.write( "Government only is  G - EG - CG + EGC = 8 - 4 - 1 + 0 = 3.    It is the answer to question (ii).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );