document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055232>Question 1055232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n(A)=13, n(A&#8746;B)=19, and n(B)=15, what is n(A&#8745;B)? &#8203;\r<BR>\n" );
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document.write( "Please explain .Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670437 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=670437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "n(A&#8745;B) = n(A) + n(B) - n(A&#8746;B) = 13 + 15 - 19 = 9.\r<BR>\n" );
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document.write( "<U>Proof</U>\r<BR>\n" );
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document.write( "It is easier to prove an equivalent equality\r<BR>\n" );
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document.write( "n(A&#8746;B) = n(A) + n(B) - n(A&#8745;B).\r<BR>\n" );
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document.write( "Let us try to count all elements in A&#8746;B.\r<BR>\n" );
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document.write( "As a first approximation, we will take  n(A) + n(B).<BR>\n" );
document.write( "But doing so, we count the elements of the intersection  n(A&#8745;B)  twice.<BR>\n" );
document.write( "So, we need distract  n(A&#8745;B)  from  n(A) + n(B), and in this way we get the exact number of elements in  A&#8746;B.\r<BR>\n" );
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document.write( "The proof is completed.\r<BR>\n" );
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document.write( "It is a classic problem of elementary set theory.\r<BR>\n" );
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document.write( "See also the lesson \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( "in this site.\r<BR>\n" );
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-I 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/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - 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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