document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203836>Question 1203836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following sets:<BR>\n" );
document.write( "U = {2, 4, 5, 6, 9, 10, 12, 16} A = {4, 5, 10, 12}<BR>\n" );
document.write( "B = {2, 4, 9, 12, 16}<BR>\n" );
document.write( "Find:<BR>\n" );
document.write( "n (A U B)<BR>\n" );
document.write( "Do not list the elements.\r<BR>\n" );
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document.write( "(I'm very confused on this problem here) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839693 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=839693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The \"n\" refers to \"number of\"<BR>\n" );
document.write( "n(A) = number of values inside set A<BR>\n" );
document.write( "n(B) = number of values inside set B<BR>\n" );
document.write( "etc\r<BR>\n" );
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document.write( "The frustrating thing about this type of set mathematics is the letter \"U\" stands for \"universal set\" and it also looks very similar to the \"union symbol\".\r<BR>\n" );
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document.write( "To avoid confusion, I'll say \"union\" when joining two sets rather than just stating the symbol.\r<BR>\n" );
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document.write( "An important set operation is set intersection. <BR>\n" );
document.write( "This is where we find what two sets have in common.<BR>\n" );
document.write( "For a venn diagram, the intersection is the overlapped area.\r<BR>\n" );
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document.write( "A = {4,5,10,12}<BR>\n" );
document.write( "B = {2,4,9,12,16}<BR>\n" );
document.write( "A intersect B = {4,12}<BR>\n" );
document.write( "This is because both 4 and 12 are in sets A and B at the same time.<BR>\n" );
document.write( "Draw out a venn diagram if needed.\r<BR>\n" );
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document.write( "Then, by the inclusion-exclusion principle, we can state the following<BR>\n" );
document.write( "n(A union B) = n(A) + n(B) - n(A intersect B)<BR>\n" );
document.write( "n(A union B) = 4 + 5 - 2<BR>\n" );
document.write( "n(A union B) = <font color=red size=4>7</font><BR>\n" );
document.write( "There are 7 elements inside set A union B<BR>\n" );
document.write( "Those 7 items are found in either:<ul><li>set A only (values 5 and 10)</li><li>set B only (values 2, 9 and 16)</li><li>or both sets A and B at the same time (values 4 and 12)</li></ul>\r<BR>\n" );
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document.write( "I know your teacher directly mentions \"do not list elements\" but I think listing things helps verify the answer.\r<BR>\n" );
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document.write( "I'll use color-coding to show how the sets union together.<BR>\n" );
document.write( "<font color=red>A = {4,5,10,12}</font><BR>\n" );
document.write( "<font color=blue>B = {2,4,9,12,16}</font>\r<BR>\n" );
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document.write( "<font color=red>A</font> union <font color=blue>B</font> = <font color=red>{4,5,10,12}</font> union <font color=blue>{2,4,9,12,16}</font><BR>\n" );
document.write( "<font color=red>A</font> union <font color=blue>B</font> = {<font color=red>4,5,10,12  </font> &nbsp;&nbsp;&nbsp;  <font color=blue> 2,4,9,12,16</font>}<BR>\n" );
document.write( "A union B = {2,4,5,9,10,12,16}<BR>\n" );
document.write( "This is where we basically glue together sets A and B. Toss out any duplicates. <BR>\n" );
document.write( "Sort the values to make life a bit easier.\r<BR>\n" );
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document.write( "To remember what \"set union\" means, what you can do is think of a marriage as a union of two people's stuff when those two people get married.<BR>\n" );
document.write( "The set {couch,fridge,tv,house} from the bride unions with the set {car,house,tv,fridge} of the groom to get {couch,tv,fridge,house,car}. <BR>\n" );
document.write( "The duplicate items are tossed. Assume that the couple can afford one of each item only.\r<BR>\n" );
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document.write( "Anyways,<BR>\n" );
document.write( "A union B = {2,4,5,9,10,12,16}<BR>\n" );
document.write( "n(A union B) = number of elements in set A union B<BR>\n" );
document.write( "n(A union B) = <font color=red>7</font><BR>\n" );
document.write( "We have confirmed the answer.\r<BR>\n" );
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document.write( "-------------------------------------------<BR>\n" );
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document.write( "Answer: <font color=red size=4>7</font><BR>\n" );
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