Question

Disjoint subsets A and B of a universal set U, except assume that n(U)=120, n(A)=45, and n(B)=50.

Then n(A′∪B)=

Answer 1

n (A' U B ) = 75

Explanation:

Here, given : n(U)=120, n(A)=45, and n(B)=50

As we know:

n (A ' U B) = n(A) − n (A∩B) ... (1)

Here, n(A) = 45

So, n( A') = n(U) - n(A) = 120 - 45 = 75

⇒ n(A') = 75

Now, as given A and B are disjoint sets.

⇒ n (A ∩ B) = Ф

So, (A' U B ) = A'

So, n (A' U B ) =n( A') = 75

⇒ n (A' U B ) = 75