Question

In a class of 80 students ,53 study art ,60 study biology ,36 study art and biology ,34 study art and chemistry ,6 study biology only and 18 study biology but not chemistry .find the students who study art only .find the number of students who study chemistry.

Answer 1

Answer:

The missing part is the intersection of all 3, label it x

Now look at the intersection of A and C, it must be 34.

But you already have x accounted for in the intersection of all 3.

So label the part in A and C, but not B as 34-x

36 study A and B, so the part of A and B, but not C is

36-x

Given that 53 study Art, in the A only part we can put

53-(36-x) - (34-x) -x = x - 17

6 study B only, put that in.

So the missing part of B is 60 - 6 - (36-x) - x

= 18

18 study B , but not C, so they could be in A

label the part of A and B, but not C as 18

BUT, we already know that A and B, not C, is 36-x

So 36-x = 18

X=18

I think we are done

Finish circle A, with A only as x-17 or