Let S = {1, 2, 3, 4, 5} and R be a relation on S where R = {(1, 1), (1, 3), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 3), (3, 5), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 5)}.
(a) Is R an order relation on S? Why or why not?
(b) Is R a partial order relation on S? Why or why not?
(c) Is R a total order relation on S? Why or why not?