Algebra.Com's Answer #788781 by ikleyn(52879)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A survey of 538 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found:\r
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document.write( "175 watched TV
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document.write( "180 hung out with friends
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document.write( "198 ate pizza
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document.write( "43 watched TV and ate pizza, but did not hang out with friends
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document.write( "43 watched TV and hung out with friends, but did not eat pizza
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document.write( "49 hung out with friends and ate pizza, but did not watch TV
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document.write( "33 watched TV, hung out with friends, and ate pizza
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document.write( "How may 18-24 year olds did not do any of these three activities last Friday night?
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document.write( "You are given an universal set U of 538 elements.\r\n" );
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document.write( "You are given 3 subsets\r\n" );
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document.write( " T of 175 elements\r\n" );
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document.write( " F of 180 elements\r\n" );
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document.write( " P of 198 elements\r\n" );
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document.write( "You are given the set of their triple intersection TFP of 33 elements.\r\n" );
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document.write( "You are given their in-pairs intersections with the triple intersection  from them\r\n" );
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document.write( " TPo with 43 elements (it is the intersection T and P with the TFP cut from it; TPo means (T and P only);\r\n" );
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document.write( " TFo with 43 elements (it is the intersection T and F with the TFP cut from it; TFo means (T and F only);\r\n" );
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document.write( " FPo with 49 elements (it is the intersection F and P with the TFP cut from it; FPo means (F and P only).\r\n" );
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document.write( "My first step is to restore in-pair intersections TP, TF an FP.\r\n" );
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document.write( "It easy to do by adding 33 elements of the triple intersection TFP to them:\r\n" );
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document.write( " TP has 43 + 33 = 76 elements;\r\n" );
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document.write( " TF has 43 + 33 = 76 elements;\r\n" );
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document.write( " FP has 49 + 33 = 82 elements.\r\n" );
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document.write( "Next I will apply the REMARCABLE formula for the union of three subsets in the universal set\r\n" );
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document.write( " n(T U F U P) = n(T) + n(F) + n(P) - n(TF) - n(TP) - n(FP) + n(TPP).\r\n" );
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document.write( "Two letters mean in-pair intersections; three letters mean a triple intersection.\r\n" );
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document.write( "Substitute the known values into the formula.\r\n" );
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document.write( " n(T U F U P) = 175 + 180 + 198 - 76 - 76 - 82 + 33 = 352.\r\n" );
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document.write( "Hence, the rest 538 - 352 = 186 do not make any of the three activities last Friday night. ANSWER\r\n" );
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document.write( "Solved.\r
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