Let X = R times R. Define a relation R on X a | vedclass

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(B) Statement-$I$: Reflexive: $(a_1, b_1) R (a_1, b_1) \Rightarrow b_1 = b_1$,which is true. Symmetric: If $(a_1, b_1) R (a_2, b_2)$,then $b_1 = b_2$,

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Statement-$I$ is true but Statement-$II$ is false.

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(B) Statement-$I$: Reflexive: $(a_1, b_1) R (a_1, b_1) \Rightarrow b_1 = b_1$,which is true. Symmetric: If $(a_1, b_1) R (a_2, b_2)$,then $b_1 = b_2$,which implies $b_2 = b_1$,so $(a_2, b_2) R (a_1, b_1)$ is true. Transitive: If $(a_1, b_1) R (a_2, b_2)$ and $(a_2, b_2) R (a_3, b_3)$,then $b_1 = b_2$ and $b_2 = b_3$,which implies $b_1 = b_3$,so $(a_1, b_1) R (a_3, b_3)$ is true. Since the relation is reflexive,symmetric,and transitive,it is an equivalence relation. Thus,Statement-$I$ is true. Statement-$II$: The set $S = \{(x, y) \in X : (x, y) R (a, b)\} = \{(x, y) \in X : y = b\}$. This represents a horizontal line $y = b$,which is parallel to the $x$-axis,not the line $y = x$. Thus,Statement-$II$ is false.

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