document.write( "Question 1055594: If n(A)=15, n(B)=18, n(C)=16, n(A∩B)=7, n(A∩C)=6, n(B∩C)=7, and n(A∪B∪C)=30 find n(A∩B∩C). \r
\n" ); document.write( "\n" ); document.write( "n(A∩B∩C)=9
\n" ); document.write( "n(A∩B∩C)=1
\n" ); document.write( "n(A∩B∩C)=2
\n" ); document.write( "n(A∩B∩C)=17
\n" ); document.write( "n(A∩B∩C)=3 \r
\n" ); document.write( "\n" ); document.write( "Please explain. Thank you \n" ); document.write( "

Algebra.Com's Answer #670758 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "From the elementary set theory, there is the formula\r\n" );
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document.write( "n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C).   (1)\r\n" );
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document.write( "or, equivalently, \r\n" );
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document.write( "n(A∩B∩C) = n(A∪B∪C) - n(A) - n(B) - n(C) + n(A∩B) + n(A∩C) + n(B∩C).   (2)\r\n" );
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document.write( "Therefore,  n(A∩B∩C) = 30 - 15 - 18 - 16 + 7 + 6 + 7 = 1. \r\n" );
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document.write( "Regarding the explanations, read the lesson\r\n" );
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document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r\n" );
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document.write( "in this site.\r\n" );
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document.write( "Everything is explained there.\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Miscellaneous word problems\". \r
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