Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and let A = {2, 3, 4, 5, 6} and B = {3, 5, 7, 8} be its subsets.

Find:

(i) A'

(ii) B'

(iii) A' ∩ B'

(iv) A' ∪ B'

Verify that:

(v) (A ∪ B)' = (A' ∩ B')

(vi) (A ∩ B)' = (A' ∪ B')

Let U = {a, b, c, d, e, f, g} be the universal set and let its subsets be A = {a, b, d, e} and B = {b, e, g}.

Verify that:

(i) (A ∪ B)' = (A' ∩ B')

(ii) (A ∩ B)' = (A' ∪ B')

Let A and B be two sets such that n(A) = 52, n(B) = 60 and n(A ∩ B) = 16. Draw a Venn diagram and find :

(i) n(A ∪ B)

(ii) n(A - B)

(iii) n(B - A)

Let P and Q be two sets such that n(P ∪ Q) = 70, n(P) = 45 and n(Q) = 38. Draw a Venn diagram and find :

(i) n(P ∩ Q)

(ii) n(P - Q)

(iii) n(Q - P)