The relation R on 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 Q from the origin } is
Answer & explanation
Correct answer: option 4
for every point p ∈ plane
distance (p from origin is same) ⇒ every $(P, P) ∈ R$ (Reflexive)
if $(P, Q) ∈ R$
distance of P form O ⇒ $(Q, P) ∈ R$ (Symmetric)
= distance of Q from O
$(P, Q) ∈ R, (Q, S) ∈ R$
⇒ distance of P form O = distance of Q from O = distance of S from O
$⇒ (P, S) ∈ R$ (Transitive)
⇒ R → equivalence relation