UPSC NDA Math Model Paper 4

Let A be the set of teachers who teach mathematics and B be the set of teachers who teach physics.
Given: n(A∪B)=20,n(A)=12, n(A∩B)=4
Here, we have to find how many teachers teach only physics ie n (B - A)As we know that, n(A∪B)=n(A)+n(B)−n(A∩B)
⇒20=12+n(B)−4
⇒n(B)=12
As we know that, n(B−A)=n(B)−n(A∩B)
⇒n(B−A)=12−4=8
So, there are 8 teachers out of 20 teachers who teach only physics
Hence, option B is the correct answer.