JEE Main 2026 — Sets and Relations Question with Solution

The relation $R$ on $A=\{0,1,2,\dots ,9\}$ is defined by $(x,y)\in R$ iff $|x-y|$ is a multiple of 3, i.e., $x\equiv y(\mathrm{mod}3)$.
Statement II:
$R$ is reflexive ($|x-x|=0$, a multiple of 3), symmetric ($|x-y|=|y-x|$), and transitive (if $x\equiv y$ and $y\equiv z(\mathrm{mod}3)$, then $x\equiv z(\mathrm{mod}3)$). So $R$ is an equivalence relation. Statement II is correct.
Statement I:
The equivalence classes are $\{0,3,6,9\}$ (4 elements), $\{1,4,7\}$ (3 elements), $\{2,5,8\}$ (3 elements).
$n(R)=4^2+3^2+3^2=16+9+9=34\ne 36$. Statement I is incorrect.