Surjection/Examples/Arbitrary Finite Set

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Example of Surjection

Let $S$ and $T$ be sets such that:

\(\displaystyle S\) \(=\) \(\displaystyle \set {a, b, c}\)
\(\displaystyle T\) \(=\) \(\displaystyle \set {x, y}\)

Let $f: S \to T$ be the mapping defined as:

\(\displaystyle \map f a\) \(=\) \(\displaystyle x\)
\(\displaystyle \map f b\) \(=\) \(\displaystyle x\)
\(\displaystyle \map f c\) \(=\) \(\displaystyle y\)

Then $f$ is a surjection.


Sources