Answer:
Let
A be the set of points in a plane.
R
= {(P, Q) : distance of the point P from the origin is same as the distance of
the point Q from the origin}
R = {(P, Q) :
|OP| = |OQ|, where Q is the origin}
Reflexive
: As |OP| = |OP|
is reflexive.
Symmetric
: Let (P, Q)
R is
symmetric.
Transitive
: Let (P, Q)
|OQ|
R is
symmetric.
Transitive
: Let (P, Q)
and
(Q, S)
R is transitive.
Hence
R is an equivalence relation.
Let
B be the set of points in a plane related to
lies on a
circle passing through P with centre O}.
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