Question

Let A be the set of all points in a plane and let O be the origin Let
`R={(p,q):OP=OQ}.` then ,R is

Answer 1

Let O be the origin and Let P,Q,X be any three points in a plane
then ,(i) OP=OP is always true . So R is transitive , .
(ii) OP=OQ`implies` OQ=OP So R is symmetric .
(iii) `(OP=OQ and OQ=OX)implies(OP=OX).` so ,R transitive .
hence ,R is an equivalence realtion .