Equivalence relation/Fiber of a mapping/Example

Let ${}M$ and ${}N$ be sets, and let ${}f\colon M\rightarrow N$ denote a mapping. In such a situation, we always get an equivalence relation on the domain ${}M$ of the mapping by declaring two elements ${}x,y\in M$ to be equivalent if they map under ${}f$ to the same element, that is, if ${}f(x)=f(y)$ holds. If the mapping ${}f$ is injective, then the equivalence relation defined by ${}f$ on ${}M$ is the equality. If the mapping is constant, then all elements from ${}M$ are equivalent under the corresponding equivalence relation.