document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203178>Question 203178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: <BR>\n" );
document.write( "A= {1,3, 5, 7}<BR>\n" );
document.write( "B= {c, d}<BR>\n" );
document.write( "S= {x e I   0 < x <10 } u {x x is a letter of the word dice} \r<BR>\n" );
document.write( "\n" );
document.write( "Find each of the following stes. <BR>\n" );
document.write( "a) A'<BR>\n" );
document.write( "b) B'<BR>\n" );
document.write( "c) A u B'<BR>\n" );
document.write( "d) (A u B)\r<BR>\n" );
document.write( "\n" );
document.write( "I am sorry I don't have all the write keys for the union and the funky looking E/ = and I don't know the correct term for it either. <BR>\n" );
document.write( "All I really need to know is what A' means. <BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153320 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=153320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A = \{1,\,3,\,5,\,7\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ B = \{c,\,d\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S = \{x\,|\,x\,\in\,\I;\,0\,<\,x\,<\,10\}\normal\,\cup\LARGE\,\{x\,|\,x\text{ is a letter in the word 'dice'}\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You didn't specify, but I suspect that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S\"> is your universe set.  It has to be, otherwise expressions like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A'\"> don't make any sense.  Given that S is the Universe set, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A'\">, read 'the complement of A', means \"everything that is in S that is NOT in A\".  The union of two sets is everything that is in one set and everything in the other set as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It will be helpful to first enumerate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S\">. First we have a set of integers, larger than zero but less than ten, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S_1 = \{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and then we have the letters of the word 'dice':\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S_1 = \{d,\,i,\,c,\,e\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Put them all together:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S = \{1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9,\,d,\,i,\,c,\,e\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From that set, cross out each element of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\"> and you are left with the complement of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\">, or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A'\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You should be able to figure out the rest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notation: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |\"> means \"such that\", <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \in\"> means \"is an element of\", <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \I\"> is the set of integers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );