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JEE Main2013MathematicsSets and RelationsActual

Let R= (3,3)(5,5),(9,9),(12,12),(5,12),(3,9) , (3,12),(3,5) be a relation on the set A= 3,5,9,12 . Then, R is :

Options

  1. Areflexive, symmetric but not transitive.
  2. Bsymmetric, transitive but not reflexive.
  3. Can equivalence relation.
  4. Dreflexive, transitive but not symmetric.

Correct answer

D. reflexive, transitive but not symmetric.

Step-by-step solution

Let R = (3,3),(5,5),(9,9),(12,12),(5,12) , (3,9),(3,12),(3,5) be a relation on set A = 3,5,9,12 Clearly, every element of A is related to itself. Therefore, it is a reflexive. Now, R is not symmetry because 3 is related to 5 but 5 is not related to 3 . Also R is transitive relation because it satisfies the property that if a R b and b R c then a R c .

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