document.write( "Question 1072460: Let the Universal set, S, have 169 elements. A and B are subsets of S. Set A has 80 elements, and set B has 75. If the total number of elements in A or B is 132, how many elements are in A, but not in B?\r
\n" ); document.write( "\n" ); document.write( "I have made a Venn Diagram, with 80 in A, and 75 in B. I am unsure how to figure out the problem from there. I have been working on it for over an hour now. \r
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Algebra.Com's Answer #687375 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The number of elements in the union A U B is\r\n" );
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document.write( "     n(A U B) = n(A) + n(B) - n(A n B),                  (*)\r\n" );
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document.write( "where (A n B) symbolizes the intersection of A and B.  By substituting the given data, you get\r\n" );
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document.write( "     132      =  80  + 75   - n(A n B),\r\n" );
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document.write( "It implies     n(A n B) = 80   +  75  - 132      = 155 - 132 = 23.\r\n" );
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document.write( "Thus you found out that the intersection  (A n B) contains 23 elements.\r\n" );
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document.write( "Therefore,   the number of elements that are in A, but not in B is 80 - 23 = 57.\r\n" );
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document.write( "Answer.  The number of elements that are in A, but not in B is  57.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding formula (*), see the lesson \r
\n" ); document.write( "\n" ); document.write( " - Counting elements in sub-sets of a given finite set\r
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\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 lessons are the part of this online textbook under the topic
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