Q. 393.8( 5 Votes )

# If sets A and B are defined as

then

A. A ∩ B = A

B. A ∩ B = B

C. A ∩ B = ϕ

D. A ∪ B = A

Answer :

**Given:**

**To find:** A ∩ B or A ∪ B

For any element of A ∩ B, A and B will have same value of y

⇒ -x^{2} = 1

⇒ x^{2} = -1

Square of any value cannot be negative

Hence, there is no value of x for which A and B will have same value of y

⇒ **A** **∩** **B =** **ϕ**

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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)

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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)

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

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Using properties of sets prove the statements given

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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.

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