# 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.

See the attached file.

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#### Solution Preview

Topology

Sets and Functions (XLV)

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#### 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.