Question

Check if the relation R in the set R of real numbers defined as R = {(a, b) : a < b} is (i) symmetric, (ii) transitive.

Answer 1

(i) It is not symmetric because if a < b then b < a is not true.

(ii) Here, if a < b and b < c then a < c is also true for all a, b, c ∈ Real numbers. Therefore, R is transitive.