JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Sets Relations and Functions

Let

A = {0, 1, 2, \dots .9)

. Let R be a relation on A defined by

(x, y) \in R

if and only if

∣ x - y ∣

is a multiple of 3.
Given below are two statements:
Statement I:

n (R) = 36

Statement II:

R

is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below

Answer: (B)

Solution

Partition

A

by remainder modulo

3

{0, 3, 6, 9}

with

4

elements,

{1, 4, 7}

with

3

, and

{2, 5, 8}

with

3

. Two elements are related exactly when they share a class, so

n (R) = 4^{2} + 3^{2} + 3^{2} = 16 + 9 + 9 = 34

, not

36

; Statement I is false. The relation is reflexive since

∣ x - x ∣ = 0

, symmetric since

∣ x - y ∣ = ∣ y - x ∣

, and transitive since a sum of multiples of

3

is a multiple of

3

, so

R

is an equivalence relation and Statement II is true. Statement I is incorrect while Statement II is correct.

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Single correct option