document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165528>Question 165528</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321331793/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Suppose B is a proper subset of C.  <BR>\n" );
document.write( "a.  If n(C) = 8, what is the maximum number of elements in B?<BR>\n" );
document.write( "b.  What is the least possible numbe rof elements in B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122085 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since \"B is a proper subset of C\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28B%29%3Cn%28C%29 ALIGN=MIDDLE  ALT=\"n%28B%29%3Cn%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie the number of elements in set B are less than the number of elements in set C)\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28B%29%3Cn%28C%29 ALIGN=MIDDLE  ALT=\"n%28B%29%3Cn%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28C%29=8 ALIGN=MIDDLE  ALT=\"n%28C%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28B%29%3C8 ALIGN=MIDDLE  ALT=\"n%28B%29%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the max number of elements in set B is 7 (since 7 is the next whole number down from 8)\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Since it is possible to have NO elements in set B (ie set B is the null set), this means that the least possible number of elements is zero. </SPAN>\n" );
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