2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3, 3)} R2 = {(3,3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)} • R3 = {(3,3), (7,7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)} • R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1,3), (3, 7)} %3D (a) Which of these relations are reflexive? If not, give a counterexample. (b) Which of these are symmetric? If not, give a counterexample. (c) Which of these are anti-symmetric? If not, give a counterexample. (d) Which of these are transitive? If not, give a counterexample. (e) Which of these are partial ordering? If not, explain why not. (f) Which of these are equivalence relations? If not, explain why not. (g) Draw the digraph of R4. (h) R2 o R4 =

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