Let’s assume we have two functions, $f : A\to B$ and $g: B\to C$ , defined for some arbitrary sets $A,B,$ and $C$ . Here is how the composite function from $A$ to $C$ , written as $g\circ f : A \to C$ , will be defined:

Let’s consider the following sets:

\begin{align*} A &= \{a, b, c, d, e\}\\ B&=\{\alpha , \beta ,\gamma \}\\ C&=\{j, k, l, m, n\}\\ D&=\{u, v, w, x, y, z\}\end{align*}

Let’s also consider the functions $f: A\to B, \: g: B\to C,$ and $h:C\to D$ , which are defined as follows:

\begin{aligned} f & = {(a, α), (b, β), (c, γ), (d, α), (e, β)} \\ g & = {(α, j), (β, m), (γ, n)} \\ h & = {(j, z), (k, y), (l, x), (m \end{aligned}

Introduction

Fundamentals

Basic Set Operations

Assessment 1

Relations

Assessment 2

Functions

Assessment 3

Indexing and Ordering of Sets

Cardinality of Sets

Assessment 4

Concluding Remarks

Composite Functions

Examples