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(B) Let $R$ be the relation defined on the set of points in a plane such that $(P, Q) \in R$ if and only if $OP = OQ$.$1$. Reflexivity: For any point

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Equivalence relation

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(B) Let $R$ be the relation defined on the set of points in a plane such that $(P, Q) \in R$ if and only if $OP = OQ$.$1$. Reflexivity: For any point $P$,$OP = OP$ is always true. Thus,$(P, P) \in R$ for all $P$. So,$R$ is reflexive.$2$. Symmetry: If $(P, Q) \in R$,then $OP = OQ$,which implies $OQ = OP$. Thus,$(Q, P) \in R$. So,$R$ is symmetric.$3$. Transitivity: If $(P, Q) \in R$ and $(Q, S) \in R$,then $OP = OQ$ and $OQ = OS$. This implies $OP = OS$. Thus,$(P, S) \in R$. So,$R$ is transitive.Since the relation is reflexive,symmetric,and transitive,it is an equivalence relation.

In a plane,two points $P$ and $Q$ are related if $OP = OQ$,where $O$ is a fixed point. The relation is:

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