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)

Question

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)

Philoid · Accepted Answer

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

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)