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JEE MainMathematicsSets and Relations

Let A = 1, 2, 3, , 20 . A relation R is defined on A A such that (a,b) R (c,d) if and only if ad = bc . The number of elements in the equivalence class containing the element (6, 8) is

Options

  1. A5
  2. B2
  3. C6
  4. D18

Correct answer

A. 5

Step-by-step solution

The equivalence class of (6,8) consists of all elements (c,d) A A such that (c,d) R (6,8) . By the definition of the relation R , we have: c 8 = d 6 8c = 6d c d = 6 8 = 3 4 Since c and d must be natural numbers, we can write c = 3k and d = 4k for some integer k 1 . We are given that c, d A , which means 1 c 20 and 1 d 20 . Substituting the expressions for c and d : 1 3k 20 k 6.66 1 4k 20 k 5 Taking the intersection of these conditions, we must have 1 k 5 . Since k is an integer, the possible values for k are 1, 2,

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