Question

Let R be a relation on a set A such that R = R^-1, then R is
1. Reflexive
2. Symmetric
3. Transitive
4. None of these

Answer 1

Correct Answer - Option 2 : Symmetric

Concept:

Properties of relation:

Let R be a relation on Z, and let x, y, z ∈ Z.

Reflexive	xRx
Symmetric	xRy implies yRx
Transitive	xRy and yRz implies xRz

Let (a, b) ∈ R

Then (a, b) ∈ R ⇒ (b, a) ∈ R^-1

(b, a) ∈ R [Because R = R^-1]

(a, b) ∈ R ⇒ (b, a) ∈ R, for all (a, b) ∈ A

aRb ⇒ bRa

∴ R is symmetric