Is the relation represented by the following digraph transit

Is the relation represented by the following digraph transitive, antisymmetric, symmetric or reflexive?

Solution

R = {(a,b),(b,c),(c,b),(c,a)}

Transitive --- No as there is no (a,b),(b,c) and (a,c). Its (c,a) in directed graph

antisymmetric ---- No as there exists (b,c),(c,b)

symmetric----- No as there is (b,c),(c,b) but no (a,b),(b,a) and (a,c),(c,a)

Reflexive ---- No as there is no (a,a),(b,b) or (c,c)