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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