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For each of the following, prove that the relation is an equivalence relation. Then give the...

For each of the following, prove that the relation is an equivalence relation. Then give the information about the equivalence classes, as specified.

a) The relation ∼ on R defined by x ∼ y iff x = y or xy = 2. Explicitly find the equivalence classes [2], [3], [−4/5 ], and [0]

b) The relation ∼ on R+ × R+ defined by (x, y) ∼ (u, v) iff x2v = u2y. Explicitly find the equivalence classes [(5, 2)] and [(1, 4)]. For fixed values a, b ∈ R+, describe [(a, b)], both as a set and geometrically

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