document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008189>Question 1008189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let the universal set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, and the following<BR>\n" );
document.write( "subsets of A :<BR>\n" );
document.write( "B is the set of elements of A multiple of 2 and less than 11.<BR>\n" );
document.write( "C is the set of elements of A that are odd and less than 10.<BR>\n" );
document.write( "D is the set {0, 1, 10, 11}.<BR>\n" );
document.write( "Determine the cardinality of the following sets. You are not obliged to justify<BR>\n" );
document.write( "your answer, but explanations can earn you partial points in case of wrong answer.<BR>\n" );
document.write( "a) C &#8746; D :<BR>\n" );
document.write( "b) B &#8746; C &#8746; D :<BR>\n" );
document.write( "c) (B \ C) &#8746; (C \ B) :<BR>\n" );
document.write( "d) (B &#8745; D) &#8746; C :<BR>\n" );
document.write( "e) (B &#8745; C) :<BR>\n" );
document.write( "f) B \ D :<BR>\n" );
document.write( "g) B &#8746; C :<BR>\n" );
document.write( "h) B &#8745; C &#8745; D :<BR>\n" );
document.write( "i) (B &#8746; C) &#8745; D :<BR>\n" );
document.write( "j) D \ (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 #623958 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=623958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first five parts (a through e) to get you started\r<BR>\n" );
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document.write( "Given Sets:\r<BR>\n" );
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document.write( "A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}\r<BR>\n" );
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document.write( "B = {0,2,4,6,8,10}\r<BR>\n" );
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document.write( "C = {1,3,5,7,9}\r<BR>\n" );
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document.write( "D = {0, 1, 10, 11}\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "C U D = {1,3,5,7,9} U {0, 1, 10, 11}\r<BR>\n" );
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document.write( "C U D = {1,3,5,7,9, 0, 1, 10, 11}\r<BR>\n" );
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document.write( "C U D = {0,1,3,5,7,9,10,11}\r<BR>\n" );
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document.write( "The cardinality is 8.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "B = {0,2,4,6,8,10}\r<BR>\n" );
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document.write( "C = {1,3,5,7,9}\r<BR>\n" );
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document.write( "D = {0, 1, 10, 11}\r<BR>\n" );
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document.write( "B U C U D = {0,2,4,6,8,10} U {1,3,5,7,9} U {0, 1, 10, 11}\r<BR>\n" );
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document.write( "B U C U D = {0,2,4,6,8,10, 1,3,5,7,9} U {0, 1, 10, 11}\r<BR>\n" );
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document.write( "B U C U D = {0,1,2,3,4,5,6,7,8,9,10} U {0, 1, 10, 11}\r<BR>\n" );
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document.write( "B U C U D = {0,1,2,3,4,5,6,7,8,9,10, 0, 1, 10, 11}\r<BR>\n" );
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document.write( "B U C U D = {0,1,2,3,4,5,6,7,8,9,10,11}\r<BR>\n" );
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document.write( "There are 12 items in the set. The cardinality of B U C U D is 12.\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "B = {0,2,4,6,8,10}\r<BR>\n" );
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document.write( "C = {1,3,5,7,9}\r<BR>\n" );
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document.write( "B \ C = {0,2,4,6,8,10}<BR>\n" );
document.write( "C \ B = {1,3,5,7,9}\r<BR>\n" );
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document.write( "Note: B and C are mutually exclusive sets, so there's nothing to kick out.\r<BR>\n" );
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document.write( "(B \ C) U (C \ B) = {0,2,4,6,8,10} U {1,3,5,7,9}\r<BR>\n" );
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document.write( "(B \ C) U (C \ B) = {0,2,4,6,8,10, 1,3,5,7,9}\r<BR>\n" );
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document.write( "(B \ C) U (C \ B) = {0,1,2,3,4,5,6,7,8,9,10}\r<BR>\n" );
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document.write( "Cardinality is 11\r<BR>\n" );
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document.write( "d)\r<BR>\n" );
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document.write( "B = {0,2,4,6,8,10}\r<BR>\n" );
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document.write( "C = {1,3,5,7,9}\r<BR>\n" );
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document.write( "D = {0, 1, 10, 11}\r<BR>\n" );
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document.write( "B &#8745; D = {0,10}\r<BR>\n" );
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document.write( "(B &#8745; D) U C = {0,10} U {1,3,5,7,9}\r<BR>\n" );
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document.write( "(B &#8745; D) U C = {0,10, 1,3,5,7,9}\r<BR>\n" );
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document.write( "(B &#8745; D) U C = {0,1,3,5,7,9,10}\r<BR>\n" );
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document.write( "Cardinality is 7\r<BR>\n" );
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document.write( "e)\r<BR>\n" );
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document.write( "Start with B = {0,2,4,6,8,10}\r<BR>\n" );
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document.write( "Erase elements found in set D. Those elements are 0 and 10 \r<BR>\n" );
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document.write( "so we end up with B \ D = {2,4,6,8}\r<BR>\n" );
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document.write( "The cardinality of this new set is 4\r<BR>\n" );
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document.write( "I'll let you handle the rest </SPAN>\n" );
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