document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945966>Question 945966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let U = {a, b, c, d, e, f} be the universal set and let A and B be subsets of U.  Suppose further that\r<BR>\n" );
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document.write( "A &#8745; B' = {b},  A &#8746; B = {a, b, c, d, f},  and A' = {a, e, f}.\r<BR>\n" );
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document.write( " Find B. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577055 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=577055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A' = {a, e, f} is given\r<BR>\n" );
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document.write( "A = {b, c, d} start with set U and erase everything in A'\r<BR>\n" );
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document.write( "We have A &#8745; B' = {b}\r<BR>\n" );
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document.write( "So that means that the element 'b' is in both set A and in set B'\r<BR>\n" );
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document.write( "Since 'b' is in set B', this means set B itself does not have 'b' inside it.\r<BR>\n" );
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document.write( "What else could be in set B? Well look at A &#8746; B = {a, b, c, d, f}\r<BR>\n" );
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document.write( "We know A = {b, c, d} from above. \r<BR>\n" );
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document.write( "Since A &#8746; B = {a, b, c, d, f}, we need an 'a' and an 'f' to fill out A &#8746; B completely.\r<BR>\n" );
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document.write( "So set B must have {a,f} at the very least. Could set B have c or d in it? It's possible since a set union can combine two sets with duplicate elements. The duplicates are tossed out.\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "So here are all the possibilities for set B\r<BR>\n" );
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document.write( "B = {a, f}<BR>\n" );
document.write( "B = {a, c, f}<BR>\n" );
document.write( "B = {a, d, f}<BR>\n" );
document.write( "B = {a, c, d, f}\r<BR>\n" );
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document.write( "Each possible set B has 'a' and 'f' in it.\r<BR>\n" );
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document.write( "It's great that we have all the possible sets for B, but unfortunately we don't have enough information to narrow down the answer to just one set. </SPAN>\n" );
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