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JEE Main202310 Apr 2023Evening ShiftMathematicsSets and RelationsActual

Let A = 2 , 3 , 4 and B = 8 , 9 , 12 . Then the number of elements in the relation R = a 1 , b 1 , a 2 , b 2 ∈ A × B , A × B : a 1 divides b 2 and a 2 divides b 1 is

Options

  1. A36
  2. B24
  3. C18
  4. D12

Correct answer

A. 36

Step-by-step solution

Given, A = 2 , 3 , 4 ,   B = 8 , 9 , 12 And a 1 ∈ A ,   b 2 ∈ B Now finding elements where a 1 divides b 2 we get, a 1 , b 2 ∈ 2 , 8 , 2 , 12 , 3 , 9 , 3 , 12 , 4 , 8 , 4 , 12 Also given, a 2 ∈ A , b 1 ∈ B Now finding elements when a 2 divides b 1 , we get, a 2 , b 1 ∈ 2 , 8 , 2 , 12 , 3 , 9 , 3 , 12 , 4 , 8 , 4 , 12 Hence, Number of relations =   6   ×   6   =   36

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