Let S be the set of all real numbers. Then the relation R ={(a, b) : 1 + ab > 0} on S is

1 + a.a = 1 + a2 > 0, ∀ a ∈ S,Therefore (a, a) ∈RTherefore R is reflexive(a, b) ∈R ⇒1 + ab > 0 ⇒ 1 + ba > 0 ⇒(b, a) ∈RTherefore R is symmetric.(a, b) ∈ R and (b, c) ∈ R need not imply (a, c) ∈ RHence, R is not transitive.