UPSC NDA Math Model Paper 10

Let Set A of people who like piano and Set B of people who like guitar and U is set of all people
Given n(A') = 15 and n(B - A) = 12
As n(A') = n(U) - n(A)
⇒ 15 = 30 - n(A)
⇒ n(A) = 15
Now, Set of people who likes at least one A∪B
n(A ∪ B) = n(A) + n(B - A)
n(A ∪ B) = 15 + 12 = 27
∴ People who do not like either of the two N = n(U) - n(A ∪ B)
N = 30 - 27 = 3