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Discrete mathematics

4. Determine whether the given relation is an equivalence relation on {1, 2, 3, 4, 5}. If the relation is an equivalence relation, list the equivalence classes. (3 points each)

(a) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 3), (3, 1)}

(b) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 3), (3, 1), (3, 4), (4, 3)}

(c) {(1, 1), (2, 2), (3, 3), (4, 4)}

(d) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 5), (5, 1), (3, 5), (5, 3), (1, 3), (3, 1)}

(e) {(x, y)|1 x 5 and 1 y 5}

(f) {(x, y)|4 divides x y}

(g) {(x, y)|3 divides x + y}