document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488902>Question 488902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. If n(A) = 8, then how many proper subsets does A have?\r<BR>\n" );
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document.write( "2. At a local college, a survey was taken to determine where students  studied on campus.  Of 180 students surveyed, it was determined that:\r<BR>\n" );
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document.write( "89 studied in the library<BR>\n" );
document.write( "76 studied in the student center<BR>\n" );
document.write( "55 studied in both places\r<BR>\n" );
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document.write( "       Of those interviewed,\r<BR>\n" );
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document.write( "a.	how many studied in only the library?\r<BR>\n" );
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document.write( "b.	how many studied in only the student center?\r<BR>\n" );
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document.write( "c.	how many did not study in either location?\r<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 #852352 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52858)</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=852352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1. If n(A) = 8, then how many proper subsets does A have?<BR>\n" );
document.write( "2. At a local college, a survey was taken to determine where students studied on campus. Of 180 students surveyed, it was determined that:<BR>\n" );
document.write( "89 studied in the library<BR>\n" );
document.write( "76 studied in the student center<BR>\n" );
document.write( "55 studied in both places<BR>\n" );
document.write( "Of those interviewed,<BR>\n" );
document.write( "a. how many studied in only the library?<BR>\n" );
document.write( "b. how many studied in only the student center?<BR>\n" );
document.write( "c. how many did not study in either location?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For part &nbsp;(1), &nbsp;tutor &nbsp;@Theo wrote a long essay, &nbsp;but his solution is &nbsp;TOTALLY &nbsp;WRONG.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring a correct solution to part &nbsp;(1).\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( "It is well known fact that every finite set of 'n' elements has precisely  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > subsets,\r\n" );
document.write( "including the empty set and the set itself as a subset.\r\n" );
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document.write( "In our problem, n = 8,  so there are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E8 ALIGN=MIDDLE  ALT=\"2%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 256 subsets, as described.\r\n" );
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document.write( "From these 256 subsets, we should exclude one subset, which is the set itself, to get <U>proper</U> subsets.\r\n" );
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document.write( "So, in this problem, there are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E8 ALIGN=MIDDLE  ALT=\"2%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 1 = 256 - 1 = 255 proper subsets.\r\n" );
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document.write( "<U>ANSWER</U>.  Set A has 255 proper subsets.\r\n" );
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document.write( "Solved correctly.\r<BR>\n" );
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