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COMEDK2024Morning ShiftMathematicsSets and RelationsActual

If A= 1,2,3,4,5 and B= 2,3,6,7 then number of elements in the set (A B) (B A) is equal to

Options

  1. A5
  2. B10
  3. C4
  4. D20

Correct answer

C. 4

Step-by-step solution

The set A B consists of all ordered pairs (a, b) where a A and b B . The set B A consists of all ordered pairs (b, a) where b B and a A . An element (x, y) belongs to (A B) (B A) if and only if (x, y) A B and (x, y) B A . This implies x A , y B , x B , and y A . Therefore, x A B and y A B . Given A = 1, 2, 3, 4, 5 and B = 2, 3, 6, 7 , the intersection A B = 2, 3 . The number of elements in A B is n(A B) = 2 . The set (A B) (B A) is equivalent to (A B) (A B) . The number of elements is n((A B) (A B)) = n(A B) n(A B)

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