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JEE Main2018MathematicsSets and RelationsActual

Consider the following two binary relations on the set A = a , b , c : R 1 = c , a , b , b , a , c , c , c , b , c , a , a and R 2 = a , b , b , a , c , c , c , a , a , a , b , b , a , c , then :

Options

  1. AR 2 is symmetric but it is not transitive
  2. Bboth R 1 and R 2 are not symmetric
  3. Cboth R 1 and R 2 are transitive
  4. DR 1 is not symmetric but it is transitive

Correct answer

A. R 2 is symmetric but it is not transitive

Step-by-step solution

Since, ( b ,   c ) ∈ R 1 but ( c ,   b ) ∉ R 1   Hence, R 1 is not symmetric. In R 1   :   b ,   c ∈ R 1 and c ,   a ∈ R 1 but b ,   a ∉ R 1 So, R 1 is not transitive. R 2 is symmetric. In R 2   :   b ,   a ∈ R 2 and a ,   c ∈ R 1 but b ,   c ∉ R 2 So, R 2 is not transitive.

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