# Birmingham Mathematics/Year 1/1VGLA/SaN

## New Notation

• ${\displaystyle :{\text{ or }}|}$ - means such that
• ${\displaystyle \in }$ - means Is a member/element of

## Introduction

A set is a collection of distinct objects. Objects that are in the set are often known as elements. For example:

• ${\displaystyle X=\{1,5,6,18\}}$
• ${\displaystyle Y=\{{\text{apple}},{\text{pear}},{\text{kewi}}\}}$
• ${\displaystyle Z=\{3,6,11,14\}}$

Two of the operations we can apply on sets are intersection (${\displaystyle \cap }$) and union (${\displaystyle \cup }$)

An intersection between two sets is defined as the set who's elements contain the common elements between the other two sets. Example using X and Z above:

${\displaystyle X\cap Z=\{6\}}$

As the only member which is in both X and Z is 6. This is sometimes known as the and operation as its the elements in both X and Z

A union between two sets is defined as the set containing the combined elements of the two sets. Example using X and Z:

${\displaystyle X\cup Z=\{1,3,5,6,11,14,18\}}$

As all of these numbers are elements of X or Z. This is sometimes known as the or operation as its elements in both X or Z