# 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

- 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 5$. Induced mappings; composition; injections; surjections; bijections: Example $5.1$