UPSC NDA Math Model Paper 10

Given, U = {1, 2, 3, ...., 20}.
Let A, B, C be the subsets of U.
A be the set of all numbers which are perfect squares
⇒ A = {1, 4, 9 16}
B be the set of all numbers which are multiples of 5
⇒ B = {5, 10, 15, 20}
and C be the set of all numbers, which are divisible by 2 and 3
⇒ C = {6, 12, 18}
Now, A ∩ B ∩ C = ϕ
So, Å, B, C are mutually exclusive.
Hence statement 1 is correct
Here Å, B, C are mutually exclusive so A, B, C can't be mutually exhaustive
Hence statement 2 is wrong
A ∪ B = {1, 4, 5, 9, 10, 15, 16, 20}
n(A ∪ B) = 8
U = {1, 2, 3, ...., 20}
n(U) = 20
Now, The number of elements in the complement set of A ∪ B = n(U) - n(A ∪ B) = 20 - 8 = 12
Hence statement 3 is correct