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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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Given: n(A) = 3, n(B) = 4 and n(A ∩ B) = 2 

(i) n(A × B) = n(A) × n(B) 

⇒ n(A × B) = 3 × 4 

⇒ n(A × B) = 12 

(ii) n(B × A) = n(B) × n(A) 

⇒ n(B × A) = 4 × 3 

⇒ n(B × A) = 12

(iii) n((A × B) ∩ (B × A)) = n(A × B) + n(B × A) – n((A × B) ∪ (B × A)) 

n((A × B) ∩ (B × A)) = n(A × B) + n(B × A) – n(A × B) + n(B × A)

n((A × B) ∩ (B × A)) = 0

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