Question

in a class of 40 students, 30 have taken science, 20 have taken mathematics and 8 has neither taken mathematic nor science, find how many students have taken. 1) both subject, 2) exactly one subject.

Answer 1

Let A be the set of students taking science and B be the set of students taking math.
n(A)=30
n(B)=20 
n((A ∪ B)')=8⇒n(A∪B)=40-8=32
1.n(A∩B)=(n(A)+n(B))-n(A∪B)
                 30+20-32=18

Answer 2

I think the answer is this Sir