document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202683>Question 202683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given  U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w}, <BR>\n" );
document.write( "and C = {l, m, n, q, r, t}, <BR>\n" );
document.write( "find (A&#8242; U C&#8242;) &#8745; B &#8242;. \r<BR>\n" );
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document.write( "I really need help on this. I have tried and tried to do this Universal Set U stuff but it is very confusing to me... Please help...<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152870 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=152870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: to add more to your confusion, the universal set U and the union operator U are actually two different symbols and stand for completely different ideas....\r<BR>\n" );
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document.write( "First, let's find A'. So form a set of elements from U but NOT in A:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A'=\left\{m, n, r, u, v, w\right\}\"> \r<BR>\n" );
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document.write( "Now let's find B'. Apply the same technique but form a set of elements from U but NOT from B:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE B'=\left\{l, m, p, q, t, u\right\}\"> \r<BR>\n" );
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document.write( "Finally, do the same for C'. Make a set from U but NOT from C:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C'=\left\{o, p, s, u, v, w\right\}\"> \r<BR>\n" );
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document.write( "-----------------\r<BR>\n" );
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document.write( "Now let's find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' \cup C'\">:\r<BR>\n" );
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document.write( "Combine the sets A' and C' and remove duplicates to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' \cup C'=\left\{m, n, o, p, r, s, u, v, w\right\}\"> \r<BR>\n" );
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document.write( "Now take the common elements from set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' \cup C'\"> and B' to get the elements: m, p, and u\r<BR>\n" );
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document.write( "Note: these elements are in BOTH sets <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' \cup C'\"> and B'\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(A' \cup C'\right) \cap B' = \left\{m, p, u\right\}\">\r<BR>\n" );
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document.write( "So the final set we're looking for is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(A' \cup C'\right) \cap B' = \left\{m, p, u\right\}\"> </SPAN>\n" );
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