Let \(X=R\times R.\) Define a relation R on X as: \(\left({a}_{1},\text{ }{b}_{1}\right)\text{ }R\text{ }\left({a}_{2},\…

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

\(\left({a}_{1},\text{ }{b}_{1}\right)\text{ }R\text{ }\left({a}_{2},\text{ }{b}_{2}\right)\text{ }\Leftrightarrow \text{ }{b}_{1}={b}_{2}.\)

Statement-I: R is an equivalence relation.

Statement-II: For some \(\left(a,b\right)\in X,\) the set

\(S=\left{\left(x,\text{ }y\right)\text{ }\in \text{ }X\text{ }:\text{ }\left(x,\text{ }y\right)\text{ }R\text{ }\left(a,\text{ }b\right)\right}\) represents a line parallel to \(y=x.\)

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