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BITSAT2013MathematicsSets and RelationsActual

Let R be the relation on the set R of all real numbers, defined by a R b If |a-b| 1 . Then, R is

Options

  1. Areflexive and symmetric only
  2. Breflexive and transitive only
  3. Cequivalence
  4. DNone of the above

Correct answer

A. reflexive and symmetric only

Step-by-step solution

Since, |a-a|=0 1, so a R a, a R R is reflexive. Now, a R b |a-b| 1 |b-a| 1 b R a R is symmetric. But R is not transitive as 1 R 2,2 R 3 but 1 R^ 3 [ |1-3|=2>1]

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