UPSC NDA Math Model Paper 4

Given, U is the universal set with 100 elements; A and B are two sets such that n(A) = 50, n(B) = 60, n(A ∩ B) = 20
We know that,
n(A' ∩ B') = n(A') + n(B') - n (A' B') .... (1)
Now,
n(A') = n(U) - n(A) = 100 - 50 = 50
n(B') = n(U) - n(B) = 100 - 60 = 40
n (A' B') = n(U) - n(A ∩ B) = 100 - 20 = 80
Equation (1) becomes,
⇒n(A' ∩ B') = 50 + 40 - 80
⇒n(A' ∩ B') = 10
Hence, if U is the universal set with 100 elements; A and B are two sets such that n(A) = 50, n(B) = 60, n(A ∩ B) = 20 then n(A' ∩ B') = 10