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COMEDK2022MathematicsSets and Relations

If A= 3,5,7 and B= 1,2,3,5 , then A B B A is equal to

Options

  1. A(3,3),(5,3),(2,7),(7,2)
  2. B(3,3),(3,5),(5,3),(5,5)
  3. C(3,3),(5,5)
  4. D(3,5),(5,5),(5,3)

Correct answer

B. (3,3),(3,5),(5,3),(5,5)

Step-by-step solution

The set A B consists of all ordered pairs (a, b) where a A and b B . Given A = 3, 5, 7 and B = 1, 2, 3, 5 , the elements of A B are pairs (a, b) such that a 3, 5, 7 and b 1, 2, 3, 5 . The set B A consists of all ordered pairs (b, a) where b B and a A . The elements of B A are pairs (b, a) such that b 1, 2, 3, 5 and a 3, 5, 7 . The intersection A B B A contains pairs (x, y) that belong to both A B and B A . This implies x A and x B , and y A and y B . The intersection of sets A and B is A B = 3, 5, 7 1, 2, 3, 5 = 3,

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