Show that the relation R in the set A of points in a plane given by `R = {(P , Q) :`distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set o

Explanation

To show that the relation \( R \) defined on the set \( A \) of points in a plane, given by

\[ R = \{(P, Q) : \text{distance of point } P \text{ from the origin is the same as the distance of point } Q \text{ from the origin}\} \]

is an equivalence relation, we need to prove that \( R \) satisfies three properties: reflexivity, symmetry, and transitivity.

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