document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092915>Question 1092915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Draw a Venn diagram and use the given information to fill in the number of elements in each region.\r<BR>\n" );
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document.write( "&#8203;n(A) = 24&#8203;, &#8203;n(B)=16&#8203;, &#8203;n(A &#8746; &#8203;B)=31, n(A')=13\r<BR>\n" );
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document.write( "Help figuring this out I got 3, 8, 15, 7 but I believe it's wrong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707556 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Draw two intersecting circles, A and B.\r\n" );
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document.write( "The circle A symbolizes (represents) the finite set A containing 24 elements.\r\n" );
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document.write( "The circle B symbolizes (represents) the finite set B containing 16 elements.\r\n" );
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document.write( "The common part of the circles A and B represents the intersection of these two sets.\r\n" );
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document.write( "By knowing that the union  (A U B)  contains 31 element, we can calculate the number of elements in the intersection (A n B).\r\n" );
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document.write( "It is  n(A n B) =  n(A) + n(B) - n(A U B) =         (1)\r\n" );
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document.write( "                =  24 + 16 - 31 = 40 - 31 = 9. \r\n" );
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document.write( "Why ?  - It is easier to me to prove an equivalent formula\r\n" );
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document.write( "n(A U B) = n(A) + n(B) - n(A n B).                  (2)\r\n" );
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document.write( "    Indeed, when we count  n(A U B)  as the sum  n(A) + n(B),  we count elements of the intersection  <U>TWICE</U>. \r\n" );
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document.write( "    Therefore, we need to subtract  n(A n B) from the sum  n(A) + n(B)  to get the exact number of elements in  n(A U B).\r\n" );
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document.write( "So, the formula (2) is proved, and, with it,  the formula (1) and the following calculations are justified.\r\n" );
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document.write( "OK.  Now we know the number of elements in the intersection (although the problem did not ask us about it. So, it is to wider your horizon).\r\n" );
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document.write( "Now to the problem question: find  n(A').\r\n" );
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document.write( "n(A') = n(A U B) - n(A) = 31 - 24 = 7.\r\n" );
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document.write( "It is so obvious that you can get it on your own if you will think 7 seconds about it looking in your plot.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "After this explanation you just know EVERYTHING about Venn diagram for two sets.\r<BR>\n" );
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document.write( "To practice and learn more, read the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lesson is the part of this online textbook under the topic \"<U>Miscellaneous word problems</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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