Algebra.Com's Answer #766612 by ikleyn(52813)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( " This problem uses VERY long (EXTREMELY long) descriptive names of the objects.\r
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document.write( " They make it intently, to confuse you.\r
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document.write( " So, to simplify the solution, you need to make two preliminary things:\r
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document.write( " - first is to give short names to these objects (subjects): call them \"category A\" and \"category B\".\r
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document.write( " - then re-formulate the problem using these short names.\r
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document.write( "Now the problem short formulation is THIS :\r\n" );
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document.write( " there are two sets A and B. Together, they comprise  of the entire universal set.\r\n" );
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document.write( " Category A is  of the entire set; category B is  of the universal set.\r\n" );
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document.write( " Questions: a) how much is the intersection (A intersection B) in terms of the universal set ?, and\r\n" );
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document.write( " b) how much is the difference of sets A \ (A intersection B) in terms of universal set ?\r\n" );
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document.write( "In the elementary set theory, there is a universal formula\r\n" );
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document.write( " m(A U B) = m(A) + m(B) - m(A intersection B). (1)\r\n" );
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document.write( "Here, \"universal\" means that it is equally applicable to any two subsets A and B of the \"parent\" set and that \"m\" is any reasonable \r\n" );
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document.write( "measure of subsets: their size relative to the \"parent\" size; or simply the number of elements in subsets; or probability; \r\n" );
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document.write( "or percentage to the \"parent\", as it is in this case.\r\n" );
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document.write( "In your given case, this basic equation (1) takes the form\r\n" );
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document.write( " 93 = 80 + 60 - m(A intersection B). (2)\r\n" );
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document.write( "You need to find m(A intersection B), (it is your first question), and from equation (2) you find it MOMENTARILY :\r\n" );
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document.write( " m(A intersection B) = 80 + 60 - 93 = 140 - 93 = 47.\r\n" );
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document.write( "The second question is to find m(A \ (A intersection B)).\r\n" );
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document.write( "Obviously, it is m(A) - m(A intersection B) = 80 - 47 = 33.\r\n" );
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document.write( "Thus the answers are 47% to the first question, and 33% to the second.\r\n" );
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document.write( "Solved, explained, completed, answered.\r
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document.write( "For your education, look into the lesson\r
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document.write( " - Counting elements in sub-sets of a given finite set\r
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document.write( "in this site. After reading this lesson, you will understand formula (1) much better.\r
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document.write( "To the tutor @EFBundy :\r
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document.write( " I like your style working at this forum.\r\n" );
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