Surjection/Examples/Arbitrary Finite Set
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Example of Surjection
Let $S$ and $T$ be sets such that:
| \(\ds S\) | \(=\) | \(\ds \set {a, b, c}\) | ||||||||||||
| \(\ds T\) | \(=\) | \(\ds \set {x, y}\) |
Let $f: S \to T$ be the mapping defined as:
| \(\ds \map f a\) | \(=\) | \(\ds x\) | ||||||||||||
| \(\ds \map f b\) | \(=\) | \(\ds x\) | ||||||||||||
| \(\ds \map f c\) | \(=\) | \(\ds y\) |
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 $5.1$