document.write( "Question 1103738: I need a Venn diagram for there are 100 people in a company. 70 are married, 80 are college grads and 60 married and college grads \n" ); document.write( "
Algebra.Com's Answer #718427 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Let
\n" ); document.write( "U = universal set
\n" ); document.write( "M = set of people who are married
\n" ); document.write( "C = set of people who are college grads\r
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\n" ); document.write( "\n" ); document.write( "Step 1) Draw a rectangle that is fairly large (say the width of your paper). This rectangle represents the entire universe U, basically the set of people we're restricting the survey to. \r
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\n" ); document.write( "\n" ); document.write( "Step 2) Draw two overlapping circles inside the rectangle. Label them M and C for \"married\" and \"college grad\" respectively. Make sure you provide a key/legend for the reader to be able to determine what M and C stand for.\r
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\n" ); document.write( "\n" ); document.write( "Step 3) In the overlapping region of the two circles, write the value 60. This represents the 60 married people who are also college grads\r
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\n" ); document.write( "\n" ); document.write( "Step 4) Write the value 10 inside circle M but NOT in circle C. How am I getting the 10? There are 70 people who are married and 60 are both married and a college grad. So there are 70-60 = 10 people who are married only and not a college grad. Notice how the values in the M circle are 10 and 60 which add back up to 60+10 = 70; the proper total number of people who are married. This confirms we have the right number. \r
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\n" ); document.write( "\n" ); document.write( "Step 5) Similarly, write the value 20 in circle C but outside of circle M. This represents those who are college grads but aren't married. It's computed by subtracting 80-60 = 20. As a check, add up everything in circle C and we get 20+60 = 80 people total who are college grads.\r
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\n" ); document.write( "\n" ); document.write( "Step 6) Add up the values in the three regions so far: 10+60+20 = 90. There are 90 people who are either married only, a college grad only, or both. This is out of 100 people so there are 100-90 = 10 people who are neither married nor a college grad. Write this value (10) inside the rectangle but outside both circles\r
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\n" ); document.write( "\n" ); document.write( "This is what the final result should look like. The numbers can move around but they must stay in the proper regions.
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\n" ); document.write( "Summary of values
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  • 100 people overall (given)
  • 70 are married (given). Some of these people are also college grads
  • 80 are college grads (given). Some of these people are also married
  • 10 people are married only and not a college grad. This is computed above and written inside circle M but not in circle C
  • 20 people are a college grad but not married. This is computed above and written inside circle C but not in circle M
  • 10 people are neither married nor a college grad (also computed above). This value is written outside the circles but inside the rectangle

\n" ); document.write( "Side Note: as a final check, you can add up all the values listed in the venn diagram to get: 10+10+60+20 = 20+80 = 100. This confirms we have the right answer as there are 100 people total.
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