Q. 515.0( 5 Votes )

# Fill in the blanks

For all sets A and B, A – (A ∩ B) is equal to ______________.

Answer :

A ∩ B’

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

**To find:** A – (A ∩ B)

A – (A ∩ B)

= A ∩ (A ∩ B)’

{∵ A – B = A ∩ B’}

= A ∩ (A’ ∪ B’)

{∵ (A ∩ B)’ = A’ ∪ B’}

= (A ∩ A’) ∪ (A ∩ B’)

{∵ Distributive property of set:

(A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)}

= Φ ∪ (A ∩ B’)

{∵ A ∩ A’ = Φ}

= A ∩ B’

**A – (A** **∩** **B) = A** **∩** **B’**

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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)

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

(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

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.

RS Aggarwal - Mathematics

If n(A) = 3 and n(B) = 5, find:

(i) The maximum number of elements in A ∪ B,

(ii) The minimum number of elements in A ∪ B.

RS Aggarwal - Mathematics

For any sets A, B and C prove that:

A × (B – C) = (A × B) – (A × C)

RS Aggarwal - Mathematics