document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868439>Question 868439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let U = {1, 2, 3, 4, 5}, A = {1, 5}, B = {1, 2, 3, 4} and C = {2, 5}. Determine<BR>\n" );
document.write( "_____  ____<BR>\n" );
document.write( "(A&#8745;B)&#8746;(B&#8746;C) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523852 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=523852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "I'm assuming that your initial problem is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Huge \overline{(A \cap B)} \cup \overline{(A \cup B)}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm going to change the notation to (A &#8745; B)' &#8746; (B &#8746; C)' so I can type it out easier.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "A = {1,5}<BR>\n" );
document.write( "B = {1,2,3,4}<BR>\n" );
document.write( "The only element that is in BOTH set A and set B is the number 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So A &#8745; B = {1}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now find the complement of set A &#8745; B. That's basically the set of everything in set U...BUT...we toss out everything we find in set A &#8745; B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we start with U = {1, 2, 3, 4, 5} and delete the element \"1\" to get (A &#8745; B)' = {2, 3, 4, 5}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B = {1, 2, 3, 4}<BR>\n" );
document.write( "C = {2, 5}\r<BR>\n" );
document.write( "\n" );
document.write( "Union sets B and C together to get {1, 2, 3, 4, 2, 5} ---> toss out duplicates ---> {1, 2, 3, 4, 5}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now find the complement of set A &#8746; B. That's basically the set of everything in set U...BUT...we toss out everything we find in set A &#8746; B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we start with U = {1, 2, 3, 4, 5} and delete the elements: 1,2,3,4,5 to get (A &#8746; B)' = { }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we're left with the empty set because we tossed out everything in U.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(A &#8745; B)' &#8746; (B &#8746; C)'\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "gets updated to \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "{2, 3, 4, 5} &#8746; { }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and that unions to \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=\"red\">{2, 3, 4, 5}</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is the final answer.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );