Mathematics - Sets and Relations Question with Solution | TestHub

Let $X=\mathbf{R}\times \mathbf{R}$. Define a relation $R$ on $X$ as : $\left(a_1,b_1\right)R\left(a_2,b_2\right)\iff b_1=b_2$ Statement I : $\mathrm{R}$ 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 :