A survey of 145 college students was done to determine their majors. Let A= the set of those majoring in art, B= the set of those majoring in biology, and C= the set of those majoring in computer science. The study revealed the following information.

n(A)=45
n(B)=55
n(C)=40
n(A∩B)=12
n(A∩C)=15
n(B∩C)=23
n(A∩B∩C)=2
How many students were not majoring in any of these disciplines?

Question

A survey of 145 college students was done to determine their majors. Let A= the set of those majoring in art, B= the set of those majoring in biology, and C= the set of those majoring in computer science. The study revealed the following information.

n(A)=45
n(B)=55
n(C)=40
n(A∩B)=12
n(A∩C)=15
n(B∩C)=23
n(A∩B∩C)=2
How many students were not majoring in any of these disciplines?

anonymous · Answer

The easiest way to do this is a Venn diagram. You'll have 3 circles, start in the center where you have n(A∩B∩C)=2, then move outwards to n(B∩C)=23 etc. but remember that since you already have two in a,b and c, the number of students in b and c  will be 23-2=21. Follow that rule when you move out to the outer circles too.

anonymous · Answer

I know how to make the diagram, but can't figure out the answer. It's either 10, 55, 53 or 63.

anonymous · Answer

Well after you finish your diagram if you all them all up you should have 92 total which leaves 145-92 out which is 53. If I did that right I ended up with 20 just in A, 22 just in B, and 4 just in C.