document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062089>Question 1062089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A equals={14,15,16,17,18,20}.<BR>\n" );
document.write( "a. How many subsets does A&#8203; have?<BR>\n" );
document.write( "b. How many proper subsets does A&#8203; have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676893 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 6 elements in A.<BR>\n" );
document.write( "a.   Therefore there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E6+=+64+ ALIGN=MIDDLE  ALT=\"+2%5E6+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > subsets of A.<BR>\n" );
document.write( "b.   There are 63 proper subsets of A (the a. answer includes all elements of A as a subset of A, which is not a proper subset).  \r<BR>\n" );
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document.write( "The number of subsets of a set of k elements is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ek ALIGN=MIDDLE  ALT=\"2%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > because each element can either be IN a subset or NOT IN a subset.   So for each element you have a binary choice whether to include it or not.  This choice applies to each of k elements, giving rise to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5Ek+ ALIGN=MIDDLE  ALT=\"+2%5Ek+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possibilities.<BR>\n" );
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