Composition of Mappings/Examples/Arbitrary Finite Sets

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Example of Compositions of Mappings

Let:

\(\displaystyle A\) \(=\) \(\displaystyle \set {1, 2, 3}\)
\(\displaystyle B\) \(=\) \(\displaystyle \set {a, b}\)
\(\displaystyle C\) \(=\) \(\displaystyle \set {u, v, w}\)


Let $\theta: A \to B$ and $\phi: B \to C$ be defined in two-row notation as:

\(\displaystyle \theta\) \(=\) \(\displaystyle \binom {1 \ 2 \ 3} {a \ b \ a}\)
\(\displaystyle \phi\) \(=\) \(\displaystyle \binom {a \ b} {w \ v}\)


Then:

$\phi \circ \theta = \dbinom {1 \ 2 \ 3} {w \ v \ w}$


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