document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202306>Question 202306</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321501073/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">  Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}.  List the elements of set\r<BR>\n" );
document.write( "\n" );
document.write( "(a) A U B<BR>\n" );
document.write( "(b) A &#8745; B    <BR>\n" );
document.write( "(c) A&#8242; &#8745; B&#8242;     <BR>\n" );
document.write( "(d) A&#8242; U B&#8242;   <BR>\n" );
document.write( "(e) A U B&#8242;   <BR>\n" );
document.write( "(f) (A U B&#8242;) &#8745; B    <BR>\n" );
document.write( "(g) (A U B) &#8745; (A U B&#8242;)\r<BR>\n" );
document.write( "\n" );
document.write( "I am having a lot of trouble with this. I promise that I have tried doing this on my own. I do not understand it at all, I can't ask a teacher because I do school online and it makes it so much harder. I read my book but I am still not understanding this.. Can you please help?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152527 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=152527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first three (there are a lot of them) to get you going in the right direction.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = {c, d, e, f}, and B = {e, f, g, h, k}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember, the big \"U\" (set union) between the two sets tells us to combine the two sets to form a new (possibly larger) set. For example, let's say we have \r<BR>\n" );
document.write( "\n" );
document.write( "the two sets \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = {1, 2, 5} and Y = {1, 3, 4, 5}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The union of these two sets is simply the combination of the two sets (remember to remove duplicates)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X U Y = {1, 2, 3, 4, 5}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The upside down U is the set intersection. This just forms a new set with any elements that the two sets have in common. So using the same sets, we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE X \cap Y = \left\{1, 5\right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take note how 1 and 5 are in both sets\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, the tick mark right after the set tells you to form a new set with every element in U that is NOT in A. In other words, form the set that has every \r<BR>\n" );
document.write( "\n" );
document.write( "letter but the ones found in the given set\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So in this case, \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' = \left\{a, b, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z\right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE B' = \left\{a, b, c, d, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z\right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------\r<BR>\n" );
document.write( "\n" );
document.write( "a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simply combine the two sets (and remove duplicates) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A \cup B = \left\{c, d, e, f, g, h, k \right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------\r<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since sets A and B only have the elements \"e\" and \"f\" in common, this means that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A \cap B = \left\{e, f\right\}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------\r<BR>\n" );
document.write( "\n" );
document.write( "c)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now since the two sets A' and B' (see above) have the elements a, b, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z in common, this means that \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A' \cap B' = \left\{a, b, c, d, g, h i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z\right\}\"><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );