venn diagram intersection of 3 sets

I have a problem to solve where .A survey of 80 students at a college showed the following:


36 take English, 32 take history, 32 take political science, 16 take history and English,


16 take political science and history, 14 take political science and English



6 take all three



Draw a Venn diagram to show the following



How many students:

a) Take only English? ____________
b) Take none of the three subjects? ____________

c) Take only History? ____________

d) Take Political Science and History but not English?___________
e) Do not take political science? __________

I have drawn my Venn diagram and am working out the answers. I am having a bit of difficulty as when calculating the numbers I do not know whether to deduct the number of people who take all three subjects from the people who take only 2 or to leave the figure alone. For instance would I say for the number of students only taking English was 36-(14+16+6)= 36-36=0, or 36-((14-6)+(16-6))=36-(8+10)= 36-18=18, or 36- (14+16)=36-30=6.
I am finding the intersection of the 3 sets difficult to work with when combine with the intersection of 2 sets. Any help would be greatly appreciated

Cheers

Neil

Start in the center and work your way out. That is, label the "all three" in the center 6.

Then, look at those that are "something and something". How many take English and Political Science?. 14

Since the 6 is in this intersection, then put 8 in the intersection of English and Poli Sci.

See what I mean?. To find how many take none of the 3, add up everything and subtract from the total number of students.

Here is the Venn. See if you can tell how I got the values.

nellyp said:

I have a problem to solve where .A survey of 80 students at a college showed the following:
36 take English, 32 take history, 32 take political science, 16 take history and English,
16 take political science and history, 14 take political science and English
6 take all three

Click to expand...

In the diagram of three overlapping circles start in the very middle with the 6. Because 16 take history and English then 10 take history and English but not political science. When done inside the English circle there should be four numbers that add up to 36.

Thanks

You are gratefully thanked for this info the starting in the middle and working out was a great tip