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MathsJEE Main 23 Jan 2026, Shift 2·Q16·MCQ·Easy–moderate

Sets, Relations & Functions · Equivalence relations

Let A={0,1,2,…,9}A = \{0, 1, 2, \ldots, 9\}. Let RR be a relation on AA defined by (x,y)∈R(x, y) \in R if and only if ∣x−y∣\lvert x - y\rvert is a multiple of 3.
Given below are two statements:
Statement I: n(R)=36n(R) = 36
Statement II: RR is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below
  1. (1)Both Statement I and Statement II are correct
  2. (2)Statement I is incorrect but Statement II is correct
  3. (3)Statement I is correct but Statement II is incorrect
  4. (4)Both Statement I and Statement II are incorrect
We corrected a printing error in the original paper

Source printed the set AA with a closing parenthesis, “2,....9)”, instead of a closing brace.

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