Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find:

(B – C)’

Let A = {a, b, c, d}, B = {c, d, e} and C = {d, e, f, g}. Then verify each of the following identities:

(i) A × (B ∩ C) = (A × B) ∩ (A × C)

(ii) A × (B – C) = (A × B) – (A × C)

(iii) (A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B)

If A and B be two sets such that n(A) = 3, n(B) = 4 and n(A ∩ B) = 2 then find.

(i) n(A × B)

(ii) n(B × A)

(iii) n(A × B) ∩ (B × A)

If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.

For any sets A and B, prove that

(A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A).

(i) If A ⊆ B, prove that A × C ⊆ B × C for any set C.

(ii) If A ⊆ B and C ⊆ D then prove that A × C ⊆ B × D.

Using properties of sets prove the statements given

For all sets A and B, (A ∪ B) – B = A – B

If A and B are two sets such that n(A) = 23, n(b) = 37 and n(A – B) = 8 then find n(A ∪ B).

In a town of 10,000 families, it was found that 40% of the families buy newspaper A, 20% buy newspaper B, 10% buy newspaper C, 5% buy A and B; 3% buy B and C, and 4% buy A and C. IF 2% buy all the three newspapers, find the number of families which buy

(i) A only,

(ii) B only,

(iii) none of A, B, and C.

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B).

Hint n(B) = n(B – A) + n(A ∩ B) ⇒ n(A ∩ B) = (39 – 13) = 26.