Let A = {1, 2, 3, 4, 5} and R be the relation on the set A and R= {(1,1), (1,3), (1,5), (2,4), (3,1), (4,3), (4,4), (5,1), (5,3))}.
Find out whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. If the relation fails to have property, provide an example showing why it fails in this case.