document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202305>Question 202305</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321501073/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Without writing them down, what are the number of subsets of the set A = {a, b, c, d, e}? Of set B = {a, b, c, d, e, f, g, h, i}? \r<BR>\n" );
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document.write( "I did not understand this question at all.. I go to school online so I do not get any help of any kind. I read all through my math book but I am so not getting this.. Can you please help?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152526 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=152526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "Recall, the number of subsets for set A is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28n%28A%29%29 ALIGN=MIDDLE  ALT=\"2%5E%28n%28A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28A%29 ALIGN=MIDDLE  ALT=\"n%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of elements in set A.\r<BR>\n" );
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document.write( "So basically, to find the number of subsets for set A, simply count the number of elements in set A and then raise that number as a power with 2 as the base.\r<BR>\n" );
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document.write( "To save ourselves from writing out <i>every</i> subset (and potentially making mistakes), we can simply use the given formula to find the number of possible subsets.\r<BR>\n" );
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document.write( "Since n(A) = 5, this means that the possible number of subsets for A is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5=32 ALIGN=MIDDLE  ALT=\"2%5E5=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So there are 32 possible subsets for A\r<BR>\n" );
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document.write( "Note: even though set A has 5 elements, this generates 32 possible subsets. So we have saved ourselves from a lot of busy work.\r<BR>\n" );
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document.write( "------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Here's a much simpler example:\r<BR>\n" );
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document.write( "Let A = {a, b, c}\r<BR>\n" );
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document.write( "The subsets of A are:\r<BR>\n" );
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document.write( "{a, b, c},<BR>\n" );
document.write( "{a, b}, {a, c}, {b, c},<BR>\n" );
document.write( "{a}, {b}, {c},<BR>\n" );
document.write( "{ }\r<BR>\n" );
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document.write( "So there are 8 subsets\r<BR>\n" );
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document.write( "Take note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3=8 ALIGN=MIDDLE  ALT=\"2%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, there are 3 elements and 2 cubed gets us 8 possible subsets. </SPAN>\n" );
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