Let \(\mathrm{X}=\mathrm{R} \times \mathrm{R}\). Define a relation R on X as: \( \left(a_1, b_1\right) R\left(a_2, b_2\r…

Let \(\mathrm{X}=\mathrm{R} \times \mathrm{R}\). Define a relation R on X as:

\(
\left(a_1, b_1\right) R\left(a_2, b_2\right) \Leftrightarrow b_1=b_2 .
\)

Statement-I: R is an equivalence relation.
Statement-II: For some \((\mathrm{a}, \mathrm{b}) \in \mathrm{X}\), the set \(S=\{(x, y) \in X:(x, y) R(a, b)\}\) represents a line parallel to \(\mathrm{y}=\mathrm{x}\).

In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2025, 23 Jan (Shift 2)]