document.write( "Question 1026852: A survey in a local college shows that of the 4000 students in the college \r
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\n" ); document.write( "\n" ); document.write( "Use a Venn diagram to find the number of people in the sets given \r
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Algebra.Com's Answer #642150 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "In these Venn diagram problems, the clues are\r\n" );
document.write( "always given in the reverse order in which you\r\n" );
document.write( "use them:\r\n" );
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document.write( "1. 4000 students in the college\r\n" );
document.write( "2. 2000 take French (F)\r\n" );
document.write( "3. 3000 take Spanish (S)\r\n" );
document.write( "4. 500 take Latin (L)\r\n" );
document.write( "5. 1500 take both French and Spanish\r\n" );
document.write( "6. 300 take both French and Latin\r\n" );
document.write( "7. 200 take Spanish and Latin\r\n" );
document.write( "8. 50 take all three languages \r\n" );
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document.write( "8. 50 take all three languages \r\n" );
document.write( "So e=50, for it is the region \r\n" );
document.write( "common to all three circles.\r\n" );
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document.write( "7. 200 take Spanish and Latin\r\n" );
document.write( "This is e+f, for they are the\r\n" );
document.write( "regions common the S and L. We\r\n" );
document.write( "already have e=50, so f=200-50\r\n" );
document.write( "or f=150.\r\n" );
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document.write( "6. 300 take both French and Latin \r\n" );
document.write( "This is d+e, for they are the\r\n" );
document.write( "regions common the F and L. We\r\n" );
document.write( "already have e=50, so d=300-50\r\n" );
document.write( "or d=250.\r\n" );
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document.write( "5. 1500 take both French and Spanish\r\n" );
document.write( "This is b+e, for they are the\r\n" );
document.write( "regions common the F and S. We\r\n" );
document.write( "already have e=50, so b=1500-50\r\n" );
document.write( "or b=1450. [There isn't enough\r\n" );
document.write( "room to write that in the region,\r\n" );
document.write( "so it'll have to stick outside of \r\n" );
document.write( "the region]\r\n" );
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document.write( "4. 500 take Latin (L)\r\n" );
document.write( "This means that there are 500 in the\r\n" );
document.write( "whole circle L = d+e+f+g. we already \r\n" );
document.write( "have that d=250, e=50, f=150, so\r\n" );
document.write( "g=500-250-50-150=50.  So g=50.\r\n" );
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document.write( "3. 3000 take Spanish (S)  \r\n" );
document.write( "This means that there are 3000 in the\r\n" );
document.write( "whole circle S = b+c+e+f. we already \r\n" );
document.write( "have that b=1450, e=50, f=150, so\r\n" );
document.write( "c=3000-1450-50-150=1350.  So c=1350.\r\n" );
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document.write( "2. 2000 take French (F)\r\n" );
document.write( "This means that there are 2000 in the\r\n" );
document.write( "whole circle F = a+b+d+e. we already \r\n" );
document.write( "have that b=1450, d=250, e=50, so\r\n" );
document.write( "c=2000-1450-250-50=250.  So a=250.\r\n" );
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document.write( "1. 4000 students in the college\r\n" );
document.write( "This means that there are 4000\r\n" );
document.write( "in the whole \"universe\", which\r\n" );
document.write( "is a+b+c+d+e+f+g+h.  We now have\r\n" );
document.write( "all but h. So \r\n" );
document.write( "h=4000-250-1450-1350-250-50-150-50=450\r\n" );
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document.write( "1. L intersect (F union S)\r\n" );
document.write( "   L ᑎ (F ᑌ S)\r\n" );
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document.write( "defg ᑎ (abde ᑌ bcef)\r\n" );
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document.write( "defg ᑎ (abcdef)\r\n" );
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document.write( "  def\r\n" );
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document.write( "d+e+f = 250+50+150 = 450\r\n" );
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document.write( "2. L' (complement)\r\n" );
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document.write( "That's everything but L:\r\n" );
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document.write( "a+b+c+h = 250+1450+1350+450 = 3500\r\n" );
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document.write( "3. F intersect S' (complement) intersect L' (complement)\r\n" );
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document.write( "(F ᑌ S') ᑎ L'\r\n" );
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document.write( "(abde ᑌ bcef') ᑎ defg'\r\n" );
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document.write( "(abde ᑌ adgh) ᑎ abch\r\n" );
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document.write( "abdegh ᑎ abch\r\n" );
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document.write( "abh\r\n" );
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document.write( "a+b+h = 250+1450+450 = 2150\r\n" );
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document.write( "Edwin
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