Question

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Answer 1

(1, 1) ∉ R, hence not reflexive (1, 2) ∈ R

⇒ (2, 1) ∈ R, also (2, 1) ∈ R

⇒ (1,2) ∈ R . (a, b) ∈ R = 9 (b, a) ∈ R,

hence symmetric

(1,2) ∈ R (2, 1) ∈ R but (1, 1) ∈ R

hence not transitive.