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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)
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)
CBSE | Class 11 | Excercise 2B | Maths | Relations | RS Aggarwal
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)

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

  • n(A × B) = n(A) × n(B)

⇒ n(A × B) = 3 × 4

⇒ n(A × B) = 12

  • 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

i

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