document.write( "Question 1165302: A survey of 1,119 tourists visiting Orlando was taken. Of those surveyed:\r
\n" ); document.write( "\n" ); document.write( "274 tourists had visited the Magic Kingdom
\n" ); document.write( "276 tourists had visited LEGOLAND
\n" ); document.write( "300 tourists had visited Universal Studios
\n" ); document.write( "94 tourists had visited both the Magic Kingdom and LEGOLAND
\n" ); document.write( "79 tourists had visited both the Magic Kingdom and Universal Studios
\n" ); document.write( "96 tourists had visited both LEGOLAND and Universal Studios
\n" ); document.write( "26 tourists had visited all three theme parks
\n" ); document.write( "How many tourists had not visited any of these three theme parks? \n" ); document.write( "
Algebra.Com's Answer #789799 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "A survey of 1,119 tourists visiting Orlando was taken. Of those surveyed:
\n" ); document.write( "274 tourists had visited the Magic Kingdom
\n" ); document.write( "276 tourists had visited LEGOLAND
\n" ); document.write( "300 tourists had visited Universal Studios
\n" ); document.write( "94 tourists had visited both the Magic Kingdom and LEGOLAND
\n" ); document.write( "79 tourists had visited both the Magic Kingdom and Universal Studios
\n" ); document.write( "96 tourists had visited both LEGOLAND and Universal Studios
\n" ); document.write( "26 tourists had visited all three theme parks
\n" ); document.write( "How many tourists had not visited any of these three theme parks?
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\n" ); document.write( "\n" ); document.write( "Solution\r
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document.write( "We have an universal set W of 1119 tourists\r\n" );
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document.write( "    and its subsets\r\n" );
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document.write( "M of 274 tourists;\r\n" );
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document.write( "L of 276 tourists;\r\n" );
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document.write( "U of 300 tourists;\r\n" );
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document.write( "   their in-pairs intersections\r\n" );
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document.write( "ML of 94 tourists;\r\n" );
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document.write( "MU of 79 tourists\r\n" );
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document.write( "LU of 96 tourists\r\n" );
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document.write( "    and finally their triple intersection\r\n" );
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document.write( "MLU of 26 tourists.\r\n" );
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document.write( "Based on this info, we can easily find the number of tourists who visited at least one of the three parks\r\n" );
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document.write( "    n(M U L U U) = m(M) + n(L) + n(U) - n(M ∩ L) - n(M ∩ U) - n(L ∩ U) + n(M ∩ L ∩ U) = \r\n" );
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document.write( "                   274 + 276 + 300 - 94 - 79 - 96 + 26 = 607.\r\n" );
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document.write( "Then the number of surveyed tourists who had not visited any of these three theme parks is the COMPLEMENT\r\n" );
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document.write( "                   1119 - 607 = 512.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "In order for to see many other similar solved problems with detailed explanations,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Challenging problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Look also into the links\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1149313.html\r
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\n" ); document.write( "\n" ); document.write( "to similar solved problems in the archive of this forum.\r
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