Let \( X = \mathbb{R} \times \mathbb{R} \). Define a relation \( R \) on \( X \) as: \( (a_1,b_1) \, R \, (a_2,b_2) \Leftrightarrow b_1 = b_2 \).
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:
