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
- Areflexive and symmetric only
- Breflexive and transitive only
- Cequivalence
- 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]