Question

Show that the relation R in the set R of Real numbers defined as R = {(a, b): a ≤ b²} is neither reflexive, nor symmetric nor transitive.

Answer 1

a ≤ a² is not true for all a. So (a, a) ∉ R hence not Reflexive.

(a, b) ∈ R ⇒ a ≤ b² does not imply that b ≤ a². So (b, a) ∉ R, hence not Symmetric. (a, b),(b, c) ∈ R ⇒ a ≤ b² and b ≤ c² does not imply that a ≤ c². So (a, c) ∉ R, hence not Transitive.