Question: Problem 3 (6 points) Part a (4 pts): Let R be the relation on the set of integers such that xRy if and only if

Problem 3 (6 points) Part a (4 pts): Let R be

Problem 3 (6 points) Part a (4 pts): Let R be the relation on the set of integers such that xRy if and only if x2-2 y2. In other words, R = { (x, ye z-ZI x2-2 yj. i. Show that R is an equivalence relation. ii. What are the equivalence classes of R? Part b (2 pts): Let A-[a, b, c, d, e). Give the smallest equivalence relation on A containing the pairs (a, c), (a, e), and (b, d) Problem 3 (6 points) Part a (4 pts): Let R be the relation on the set of integers such that xRy if and only if x2-2 y2. In other words, R = { (x, ye z-ZI x2-2 yj. i. Show that R is an equivalence relation. ii. What are the equivalence classes of R? Part b (2 pts): Let A-[a, b, c, d, e). Give the smallest equivalence relation on A containing the pairs (a, c), (a, e), and (b, d)

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