A and B are subsets of a universal set U such that nA 58 nB

A and B are subsets of a universal set U such that n(A) = 58, n(B) = 52, n ((AUB)\') = l00, and n(U) = 177. How many elements of U are in exactly one of the subsets A and B?

Solution

First, note that

n(A U B) = n(U) - n(A U B)\' = 177 - 100 = 77

Now, also,

n(A n B) = n(A) + n(B) - n(A U B) = 58+52-77 = 33

Thus, those in exactly one set is

n(A only or B only) = [n(A) - n(A n B)] + [n(B) - n(A n B)]

n(A only or B only) = [58-33]+[52-33] = 25 + 19

= 44 [ANSWER]