document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117994>Question 1117994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jogn was trying to find out who in the  Kansas City area liked the Philadelphia Phillies  and the Kansas City Royals baseball teams. He interviewed 150 people. He found that:\r<BR>\n" );
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document.write( "- 83 liked the Phillies.<BR>\n" );
document.write( "- 107 liked the Royals.<BR>\n" );
document.write( "- 54 liked both the Phillies and the Royals.\r<BR>\n" );
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document.write( "a. How many liked only the Phillies?<BR>\n" );
document.write( "b. How many liked only the Royals?<BR>\n" );
document.write( "c. How many did not like either the Phillies or the Royals?\r<BR>\n" );
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document.write( " Draw a Venn Diagram and solve. \r<BR>\n" );
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document.write( "P.S. - This section is called, \"Application of Sets\". Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733225 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52810)</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=733225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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( "In this case, Venn diagram consists of two intersecting circles, concluded into larger rectangle.\r\n" );
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document.write( "One circle represents those 83 who like P.\r\n" );
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document.write( "The other circle represents those 107 who like R.\r\n" );
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document.write( "The intersection of circles represents those 54 who like both.\r\n" );
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document.write( "The entire rectangle represents those 150 who were interviewed.\r\n" );
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document.write( "As soon as you will draw the sketch of the diagram, the solution is clear to you:\r\n" );
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document.write( "    a. How many liked only the Phillies?                          83 - 54 = 29.\r\n" );
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document.write( "    b. How many liked only the Royals?                           107 - 54 = 53.\r\n" );
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document.write( "    c. How many did not like either the Phillies or the Royals?  150  - 83 - 107 + 54 = 14.\r\n" );
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document.write( "Only the last calculation requires some explanation  (the \"a\" and \"b\" are OBVIOUS).\r\n" );
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document.write( "To calculate those inside the rectangle, who don't like  P or R, we subtract the population of both circles from the rectangle.\r\n" );
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document.write( "But since we subtract the intersection TWICE, we are oblige to add the value of this intersection one time.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "-----------------------<BR>\n" );
document.write( "To see other similar solved problems, &nbsp;look into the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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