Show that the relation R in R defined as R ={(a, b); a ≤ b} is reflexive and transitive but not symmetric

{(a, b); a ≤ b}

(i)  R is reflexive, a ≤ a ⇒ a =a is true

(ii) R is not symmetric; a ≤ a ⇒ b ≤ a, which is not true, e.g.: 3 < 5, but 5 is not less than 3.

(iii) R is transitive, If a ≤ b ⇒ b ≤ a,   then a ≤ c e.g. 2 < 3, 3 < 4, ⇒ 2 < 4..