document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209457>Question 1209457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> List all subsets of {A,B,C,D} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848873 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=848873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "List all subsets of {A,B,C,D}<BR>\n" );
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document.write( "It has one empty subset {}.\r<BR>\n" );
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document.write( "It has 4 (four) subsets consisting of one element.\r<BR>\n" );
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document.write( "These subsets are {A}, {B}, {C}, and {D}.\r<BR>\n" );
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document.write( "It has 6 (six) subsets consisting of two elements.\r<BR>\n" );
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document.write( "These subsets are {A,B}, {A,C}, {A,D}, {B,C}, {B,D}, {C,D}.\r<BR>\n" );
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document.write( "It has 4 (four) subsets consisting of three elements.\r<BR>\n" );
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document.write( "These subsets are {A,B,C}, {A,B,D}, {A,C,D}, {B,C,D}.\r<BR>\n" );
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document.write( "We obtain this list simply crossing out letter by letter from the list of 4 elements {A,B,C,D}.\r<BR>\n" );
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document.write( "Finally, the original set {A,B,C,D} has a unique subset {A,B,C,D}, which consists of 4 elements.\r<BR>\n" );
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document.write( "This subset is special: it is called \"improper\" subset.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Notice that the total number of subsets is &nbsp;&nbsp;1 + 4 + 6 + 4 + 1 = 16 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4 ALIGN=MIDDLE  ALT=\"2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;including empty subset and improper subset.\r<BR>\n" );
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document.write( "It is not a random coincidence and it is not accidently.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The general fact is that the number of all subsets of any finite set of \"n\" elements is  &nbsp;<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;\" >,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;including empty subset and improper subset.\r<BR>\n" );
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