Question: Let X be a set and f : X R be a real-valued function. Show that the relation givenby x y if and only if

Let X be a set and f : X R be a real-valued function. Show that the relation givenby x y if and only if f(x) = f(y) is an equivalence relation on X.Remark: Equivalence classes for this relation are called level sets of f.

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