Let X = R × R. Define a relation R on X as: $\left({\mathrm{a}}_1,{\mathrm{b}}_1\right)\mathrm{R}\left({\mathrm{a}}_2,{\mathrm{b}}_2\right)\iff {\mathrm{b}}_1={\mathrm{b}}_2.$
Statement-I : R is an equivalence relation. 
Statement-II : For some $(\mathrm{a},\mathrm{b})\in \mathrm{X}$, the set  $\mathrm{S}=\left\{\right(\mathrm{x},\mathrm{y})\in \mathrm{X}:(\mathrm{x},\mathrm{y}\left)\mathrm{R}\right(\mathrm{a},\mathrm{b}\left)\right\}$ represents a line parallel to y = x. 
In the light of the above statements, choose the correct answer from the options given below: