Set Theory Venn Diagram I have a question : A survey conducted on 1000 people. It turned out that 595 members of the Democratic, 595 wear eye glasses and 550 like the ice cream.395 people are members of the democrat who wear glasses, 350 members of the democrat who likes ice cream, and 400 people wear glasses and like ice cream, 250 of them are members of the democrat who wear glasses and like ice cream. 
How many people are members of democrat do not wear glasses and do not like ice cream? 
 A: You want to work from the inside-out when making a Venn diagram for these types of problems. EDIT: I realized after making the diagrams that it should be democrat instead of democratic... but you should still get the idea.
First, mark where all three agree. You are given that 250 of them are democratic, wear glasses and like ice cream. This means we have a 250 where all three circles meet.
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Now, work out the common traits between two circles. Let's first focus on members who are democratic and were glasses. I will mark this in yellow. 
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You are given that 395 people are democratic and wear glasses. This means the entire yellow section must add up to get 395. Knowing that, we can find the rest of the yellow section by subtracting 250 from 395. 
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Do the same thing for the other pairings of two circles. Let's now focus on members who are democratic and like ice cream. I will mark this in yellow. 
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You are given that 350 members are democratic and like ice cream. Just like before, this means the yellow section must have a total of 350. Subtracting 250 from 350 gives the missing common amount of 100.
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The last common area is between members who wear glasses and like ice cream. I will mark this in yellow. 
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We know 400 members wear glasses and like ice cream. This gives us the rest of the common section as follows. 
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We are now left with the outer circles. These are members who are one thing only. 
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You want to find how many people are democratic, but do not wear glasses and do not like ice cream. This is the outer section of the green circle. We know all of the sections of the green circle have to add up to 595. How would you find the missing outer section?
