Q22Multiple correct5 Marks25 Feb 2024

Consider the following relations defined on the set of integers: $R_1=\{(x,y):x,y\in\mathbb{Z}\text{ and }|x-y|\leq 3\}$. $R_2=\{(x,y):x,y\in\mathbb{Z}\text{ and }3\text{ divides }x-y\}$. Choose the correct option(s):

A

$R_1$ is reflexive and symmetric.

B

$R_2$ is symmetric but not transitive.

C

$R_1$ is an equivalence relation but $R_2$ is not an equivalence relation.

D

$R_2$ is an equivalence relation but $R_1$ is not an equivalence relation.