If A and B are two sets such that n(A) = 37, n(B) = 26 and n (A ∪ B) = 51, find n (A ∩ B).

Let A = {2, 3, 5, 7, 11, 13}, B = {5, 7, 9, 11, 15} be subsets of U = {2, 3, 5, 7, 9, 11, 13, 15}.

Using Venn diagrams, verify that:

(i) (A ∪ B’) = (A’ ∩ B’)

(ii) (A ∩ B)’ = (A’ ∪ B’)

Using Venn diagrams, show that (A – B), A ∩ B) and (B – A) are disjoint sets, taking A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12, 15, }.

If P and Q are two sets such that n(P ∪ Q) = 75, n (P ∩ Q) = 17 and n(P) = 49, find n (Q).

If A and B are two sets such that n(A) = 24, n(B) = 22 and n(A ∩ B) = 8, find:

(i) n(A ∪ B)

(ii) n(A – B)

(iii) n(B – A)