Question

R : {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}. Check if R is

(i) reflexive

(ii) symmetric

(iii) transitive

Answer 1

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}

(i) Here, (x, x) ∈ R, for x ∈ {1, 2, 3}

∴ R is reflexive.

(ii) Here, (1, 2) ∈ R, but (2, 1) ∉ R.

∴ R is not symmetric.

(iii) Here, (1, 2), (2, 3) ∈ R, But (1, 3) ∉ R.

∴ R is not transitive.