document.write( "Question 1047210: Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where:?\r
\n" ); document.write( "\n" ); document.write( "A={2,5,6,7,14,18,20}
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\n" ); document.write( "C={1,2,3,4,6,10,12,14,15,16,17,20} \r
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\n" ); document.write( "\n" ); document.write( "Find the number of elements in the set (A∩C) ∩ B n[(A∩C)∩Bc] \n" ); document.write( "
Algebra.Com's Answer #662725 by AnlytcPhil(1807)\"\" \"About 
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document.write( "Find the number of elements in the set\r\n" );
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document.write( " (A∩C) ∩ B ∩ [(A∩C) ∩ Bc]\r\n" );
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document.write( "First we find \r\n" );
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document.write( "A∩C = {2,5,6,7,14,18,20} ∩ {1,2,3,4,6,10,12,14,15,16,17,20} \r\n" );
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document.write( "Take the elements in common to A and C:\r\n" );
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document.write( "A∩C = {2,6,14,20}\r\n" );
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document.write( "We find Bc = B={1,3,4,5,7,8,9,10,11,17,20}c\r\n" );
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document.write( "That's the set of all elements in the universal set S\r\n" );
document.write( "which are not elements of B\r\n" );
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document.write( "S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}\r\n" );
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document.write( "So \r\n" );
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document.write( "Bc = {2,6,12,13,14,15,16,18,19} \r\n" );
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document.write( "We find (A∩C) ∩ B\r\n" );
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document.write( "(A∩C) ∩ B = {2,6,14,20} ∩ {1,3,4,5,7,8,9,10,11,17,20}\r\n" );
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document.write( "By taking the elements in common:\r\n" );
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document.write( "(A∩C) ∩ B = {20}  (There's only one!)\r\n" );
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document.write( "Next we find\r\n" );
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document.write( "[(A∩C) ∩ Bc] = {2,6,14,20} ∩ {2,6,12,13,14,15,16,18,19}\r\n" );
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document.write( "Taking the elements in common:\r\n" );
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document.write( "[(A∩C) ∩ Bc] = {2,6,14} \r\n" );
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document.write( "So\r\n" );
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document.write( " (A∩C) ∩ B ∩ [(A∩C) ∩ Bc]\r\n" );
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document.write( "      {20} ∩ {2,6,14}\r\n" );
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document.write( "There are no elements in common, so the answer \r\n" );
document.write( "is the empty set:\r\n" );
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document.write( "Answer = n(Ø) which is 0. \r\n" );
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document.write( "Edwin
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