document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164827>Question 1164827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My Question is: Let X = {1,2,...,n}, A = {A⊆X | n ∉ A} and B = {A⊆ X | n ∈ A}. Show that |A|=|B| by (BP).\r<BR>\n" );
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document.write( "(I understand what each set means where A is the set where n is not included and B is the set where n is included, I believe I am only counting the subsets of each set and not the elements in each set but im not sure how to do that exactly) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789270 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "What you wrote is \"Show that the cardinality of set A is equal to the cardinality of set B\", that is the number of elements in A is equal to the number of elements in B, which is not true.  Set B has n elements and Set A has n - 1 elements.  You cannot prove that the number of subsets of A is equal to the number of subsets of B, because that is not a true statement either.\r<BR>\n" );
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document.write( "There are twice as many subsets in B as in A because the number of subsets in A is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^{n-1}\"> and the number of subsets in B is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^n\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{2^n}{2^{n-1}}\ =\ 2\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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