Question

Two points $P$ and $Q$ in a plane are related if $OP=OQ$, where $O$ is a fixed point. This relation is

• A. Reflexive but symmetric
• B. Symmetric but not transitive
• C. An equivalence relation
• D. None of these

Answer 1

Answer: (C)

An equivalence relation

i) Since $OP=OP,$ the relation is reflexive

ii) If $OP=OQ$ then $OQ=OP$ also

Therefore if $P$ is related to $Q$ then $Q$ is related to $P$ also
Hence relation is symmetric

iii) Let $P$ be related to $Q$ and $Q$ be related to $R$

$\Rightarrow OP=OQ$ and $OQ=OR$

$\Rightarrow OP=OR$, $P$ is related to $R$

Hence, the given relation is an equivalence relation.