Consider two subsets P and Q of a universal set U. Given that n(U) = 104, n(P) = 63, n(P'∩Q) = 28 and n(P∩Q) = 16, find: (a) n(Q)

Answer 1

First, we must note that the set Q can be written as Q = (P∩Q) ∪ (P'∩Q) [it's important to note that the sets (P∩Q) and (P'∩Q) are disjoint subsets of Q]. Next, we use the given values for n(P∩Q) and n(P'∩Q) to find that n(Q) = n((P∩Q) ∪ (P'∩Q))

= n(P∩Q) + n(P'∩Q) (true since (P∩Q) and (P'∩Q) are disjoint subsets of Q)

= 16 + 28

= 44