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Symmetric Relations

Two points ...

Question

Two points $A$ and $B$ in a plane are related if $O A = O B,$ where $O$ is a fixed point. This relation is

A

partial order relation

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B

equivalence relation

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C

reflexive but not symmetric

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D

refleve but not transitive.

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Solution

The correct option is A equivalence relation
$O A = O A,$ it is Reflexive

$O A = O B \Rightarrow O B = O A .$ it is symmetric

Now $O A = O B, O B = O C \Rightarrow O A = O C,$ it is transitive

R, S, T,i.e. equivalence relation.
Ans: B

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