document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001910>Question 1001910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If |P| = 10, |Q| = 12, and |P &#8746;Q| = 15, what is |P &#8745;Q|?pls help with a little explanation.thanks in advance and more power. </SPAN>\n" );
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document.write( "If |P| = 10, |Q| = 12, and |P &#8746;Q| = 15, what is |P &#8745;Q|?pls help with a little explanation.thanks in advance and more power.<BR>\n" );
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document.write( "If &nbsp;P&nbsp; and &nbsp;Q&nbsp; are non-intersecting sets of elements, &nbsp;then it would be &nbsp;10 + 12 = 22 \r<BR>\n" );
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document.write( "elements in their union. &nbsp;But there are only &nbsp;15&nbsp; elements in the union.\r<BR>\n" );
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document.write( "It means that &nbsp;P&nbsp; and &nbsp;Q&nbsp; have a non-empty intersection.\r<BR>\n" );
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document.write( "Let &nbsp;x&nbsp; be the number of elements in the intersection &nbsp;|P &#8745;Q|. \r<BR>\n" );
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document.write( "Let &nbsp;p&nbsp; be the number of elements of &nbsp;P&nbsp; that are NOT in &nbsp;Q, &nbsp;and \r<BR>\n" );
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document.write( "let &nbsp;q &nbsp;be the number of elements of &nbsp;Q&nbsp; that are NOT in &nbsp;P.\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "p + x = 10, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)\r<BR>\n" );
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document.write( "q + x = 12, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "p + q + x = 15 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3) \r<BR>\n" );
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document.write( "(for the union &nbsp;|P &#8746;Q|).\r<BR>\n" );
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document.write( "Add (1) and (2). &nbsp;You will get\r<BR>\n" );
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document.write( "p + q + 2x = 22. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(4).\r<BR>\n" );
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document.write( "Now distract (3) from (4). &nbsp;You will get \r<BR>\n" );
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document.write( "x = 22 - 15 = 7.\r<BR>\n" );
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document.write( "<U>Answer</U>. &nbsp;There are &nbsp;7&nbsp; elements in the intersection of &nbsp;P&nbsp; and &nbsp;Q: &nbsp;|P &#8745;Q| = 7.\r<BR>\n" );
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