### Introduction

If we can identify a property which is common to several objects, it is often useful to group them together. Such a grouping is called a
**
set
**
. Engineers for example, may wish to study all components of a production run which fail to meet some specified tolerance. Mathematicians may look at sets of numbers with particular properties, for example, the set of all even numbers, or the set of all numbers greater than zero. In this block we introduce some terminology that is commonly used to describe sets, and practice using set notation. This notation will be particularly useful when we come to study probability in Section 35.2.

#### Prerequisites

- have knowledge of basic algebra

#### Learning Outcomes

- state what is meant by a set
- use set notation
- explain the concepts of the intersection and union of two sets
- define what is meant by the complement of a set
- use Venn diagrams to illustrate sets

#### Contents

1 Sets1.1 Subsets

1.2 The symbol $\in $

1.3 The empty set and the universal set

1.4 The complement of a set

2 Venn diagrams

3 The intersection and union of sets

3.1 Intersection

3.2 Union