If R is a relation on the set R of all real numbers, defined by aRb if |a − b| ≤ 1, then R is
A
Reflexive and symmetric
B
Symmetric only
C
Transitive only
D
Asymmetric
Correct Option:
A
Explanation
The relation is defined by aRb if |a − b| ≤ 1. It is reflexive because |a − a| = 0 ≤ 1, and symmetric because |a − b| = |b − a|. It is not necessarily transitive: for example, 0R1 and 1R2, but 0 is not related to 2, since |0 − 2| = 2 > 1.
