Let U be a universal set with disjoint subsets A and B with n(U ) = 55, n(A) = 25, and n(B) = 10.

Question

(a) Find n(A ∩ B) (b) Find n(A′ ∪ B)

Answer 1

Hello Ang,

If there are 55 items in the universal set, 25 in set A and 10 in set B, then there are 20 items that are not in either set A or B. Since A and B are disjoint, they don't share any items.

a.) n(A ∩ B) must be 0 because the sets are disjoint. No items are shared.

b.) n(A' ∪ B) must be 30. If there are 25 items in A, then there must be 30 items in A' since there are 55 items total. Now, B is a subset of A'. The 10 items in B are also a part of A', so the union of a set (A') and one of its subsets (B) must just contain the elements in A'. So, your answer is 30.

Hope this helps,

Jim