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JEE Main202229 Jun 2022Morning ShiftMathematicsSets and RelationsActual

Let a set A = A 1 ∪ A 2 ∪ … ∪ A k , where A i ∩ A j = ϕ for i ≠ j ; 1 ≤ i , j ≤ k . Define the relation R from A to A by R = x , y : y ∈ A i if and only if x ∈ A i , 1 ≤ i ≤ k . Then, R is:

Options

  1. Areflexive, symmetric but not transitive
  2. Breflexive, transitive but not symmetric
  3. Creflexive but not symmetric and transitive
  4. Dan equivalence relation

Correct answer

D. an equivalence relation

Step-by-step solution

Let A = 1 , 2 , 3 Then R = 1 , 1 , 1 , 2 , 1 , 3 2 , 1 , 2 , 2 , 2 , 3 3 , 1 , 3 , 2 3 , 3 which is an equivalence relation.

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