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JEE Main201815 Apr 2018Morning ShiftMathematicsSets and RelationsActual

Consider the following two binary relations on the set A= a, b, c : R₁= ( 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. AR₂ is symmetric but it is not transitive
  2. BBoth R₁ and R₂ are transitive
  3. CBoth R₁ and R₂ are not symmetric
  4. DR₁ is not symmetric but it is transitive

Correct answer

A. R₂ is symmetric but it is not transitive

Step-by-step solution

Both R₁ and R₂ are symmetric as For any (x, y) R₁ , we have (y, x) R₁ and similarly for R₂ Now, for R₂,(b, a) R₂,(a, c) R₂ but (b, c) R₂ . Similarly, for R₁,(b, c) R₁,(c, a) R₁ but (b, a) R₁ . Therefore, neither R₁ nor R₂ is transitive.

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