# Composition of Mappings/Examples/Arbitrary Finite Sets

## Example of Compositions of Mappings

Let:

 $\ds A$ $=$ $\ds \set {1, 2, 3}$ $\ds B$ $=$ $\ds \set {a, b}$ $\ds C$ $=$ $\ds \set {u, v, w}$

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

 $\ds \theta$ $=$ $\ds \binom {1 \ 2 \ 3} {a \ b \ a}$ $\ds \phi$ $=$ $\ds \binom {a \ b} {w \ v}$

Then:

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