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    To show that the function f is an equivalence relation

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    Topology
    Sets and Functions (XLV)
    Functions

    Let f : X --> Y be an arbitrary mapping. Define a relation in X as follows:
    x_1 ~ x_2 means that f(x_1) = f(x_2).
    Show that this is an equivalence relation and describe the equivalence sets.

    See the attached file.

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    https://brainmass.com/math/geometry-and-topology/show-function-equivalence-relation-147333

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    Topology
    Sets and Functions (XLV)
    ...

    Solution Summary

    This solution is comprised of a detailed explanation of the properties of the mappings.
    It contains step-by-step explanation of the following problem:

    Let f : X --> Y be an arbitrary mapping.
    Define a relation in X as follows:
    x_1 ~ x_2 means that f(x_1) = f(x_2).
    Show that this is an equivalence relation and describe the equivalence sets.

    $2.19