Let $X=\mathbf{R} \times \mathbf{R}$. 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 $(a, b) \in X$, the set $S=\{(x, y) \in X:(x, y) R(a, b)\}$ represents a line parallel to $y=X$.
In the light of the above statements, choose the correct answer from the options given below :