Q. 173.6( 10 Votes )

# Determine whether each of the statement in

For all sets A, B and C, if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C

Answer :

**Given:** There are three sets A, B and C

**To check:** if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C is true or false

Let x ∈ A ∪ B

⇒ x ∈ A or x ∈ C

⇒ x ∈ C or x ∈ C {∵ A ⊂ C and B ⊂ C}

⇒ x ∈ C

⇒ A ∪ B ⊂ C

**Hence, the given statement is true**

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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