A set is a collection of objects. These objects, called the members or elements of the set, are enclosed in a special type of bracket, called braces {...} and are separated by commas. The order of the elements in not important.
Notation
A set can be described in one of three ways:
1. In words: A = {the first three whole numbers}
2. By listing each member: A = {0, 1, 2}
3. In set builder notation, which states the rules of membership.
A = {x: x < 3, x W}
Symbols
Symbol

Meaning

Example

U or E

the universal set  the set of all elements or members being considered. 
Ø or {}

the empty or null set  This set has no elements or members. 
is a member of  2 {even numbers}  
is not a member of  3 {even numbers}  
is a subset of All of the sets that can be made using elements of the set. Includes the empty set and the original set. 
{3, 4} {2, 3, 4} 

n(A)

the cardinal number (number of members) of set A. 
if A = {4, 5, 6, 7, 8} 
A'

the complement of set A. All the members not in set A. 
If A = {4, 5, 6, 7, 8} and the universal set is {whole numbers less than 10} then A' = {0, 1, 2, 3, 9} 
the union of sets. Every element from EACH set. 
If A = {4, 5, 6, 7, 8} and B = {3, 4, 5} then 

∩

the intersection of sets. 
If A = {4, 5, 6, 7, 8} and B = {3, 4, 5} then A ∩ B = {4, 5} 
Types of Sets
Venn Diagrams
Venn diagrams are useful for showing sets, solving problems and situations involving probability. These are covered in detail in Year 12, Topic 59.