Let U U be a universal set with disjoint subsets A A and B B such that n(A)=40 n ( A ) = 40 , n(A′)=44 n ( A ′ ) = 44 , and n(B′)=69 n ( B ′ ) = 69 . Find the number of elements in A∪B A ∪ B .

Answer 1

To find this, we must find the number of elements in set B and add this to the number of elements in set A (n(A)=40). Remember that because A and B are disjoint, n(A∩B) = 0, so we don't need to worry about subtracting that term. Since A and A' encompass all of the Universal set, n(U) = n(A) + n(A') = 40+44 = 84. Then, likewise, because n(B) + n(B') = n(U), n(B) = n(U) - n(B') = 84-69 = 15.

Therefore, n(A∪B) = n(A) + n(B) = 40+15 = 55.