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 : \(\quad \mathrm{R}\) 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 :

1. A Both Statement I and Statement II are false
2. B Statement I is true but Statement II is false
3. C Both Statement I and Statement II are true
4. D Statement I is false but Statement II is true