Two points A and B in a plane are related if OA = OB, where O is fixed point, this relation is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Equivalence relation
(1) Reflexive
as for ∀ A ∈ plane, OA = OA ⇒ (A, A) ∈ Relation
(2) Symmetric
for every (A, B) ∈ Relation, OA = OB ⇒ OB = OA
⇒ (B, A) ∈ Relation
(3) Transitive
(A, B) ∈ Relation, (B, C) ∈ Relation ⇒ OA = OB = OC
⇒ OA = OC ⇒ (A, C) ∈ R
⇒ Equivalence relation