Q. 404.1( 7 Votes )

# If A and B are two sets, then A ∩ (A ∪ B) equals

A. A

B. B

C. ϕ

D. A ∩ B

Answer :

**Given:** A and B are two given sets

**To find:** A ∩ (A ∪ B)

Let x ∈ A ∩ (A ∪ B)

⇒ x ∈ A and x ∈ (A ∪ B)

⇒ x ∈ A and (x ∈ A or x ∈ B)

⇒ (x ∈ A and x ∈ A) or (x ∈ A and x ∈ B)

⇒ x ∈ A or x ∈ A ∩ B

⇒ x ∈ A

Hence, **A** **∩** **(A** **∪** **B) = A**

Rate this question :

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)

RS Aggarwal - Mathematics

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)

RS Aggarwal - Mathematics

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

RS Aggarwal - Mathematics(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.

RS Aggarwal - Mathematics

Using properties of sets prove the statements given

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

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

Hint n(A) = n(A – B) + n(A ∩ B) n(A ∩ B) = (23 – 8) = 15.

RS Aggarwal - Mathematics

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

RS Aggarwal - Mathematics