Define a relation on the set of real numbers by

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define a relation

R

on the set of real numbers

\mathbb{R}

xRy\iff x-y\in\mathbb{Z}

. Which of the following is true for

R

? (a)

R

is reflexive and symmetric but not transitive (b)

R

is reflexive only (c)

R

is reflexive, symmetric and transitive (d)

R

is symmetric only