Question

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

Answer 1

Solution: R is reflexive, since (1, 1), (2, 2) and (3, 3) lie in R. Also, R is not symmetric,as (1, 2) ∈ R but (2, 1) ∉ R. Similarly, R is not transitive, as (1, 2) ∈ R and (2, 3) ∈ Rbut (1, 3) ∉ R