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To show that the function f is an equivalence relation

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.

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Topology
Sets and Functions (XLV)
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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.

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