A set is a collection of data. Values that belong to a set are shown inside curly brackets { }.

A set might not contain numbers. It might contain items such as the colours of a flag or makes of cars. Values in a set are known as elements. A set called A can be defined as A = {red, white, blue}. The number of elements in this set is given by n(A), which in this case is 3.

There are two ways to define sets. They can be shown as a list:

A = {red, white, blue},

or the list can be derived:

B = {x | 0 < x < 10},

where the vertical bar | means such that. Sometimes the vertical bar might be shown as a colon : .

A set that contains all possible elements for a given situation is a Universal Set, and is written as `xi`. A universal set that contains all the scores that can be thrown with two dice is: `xi = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}`

Sets can be joined together: there can be a Union of sets or an Intersection of sets.

`O uu P` is read as O union P, and identifies the elements that are in set O OR in set P or in both. Elements in both sets are only listed once:

`O = {1, 3, 5, 7, 9, 11}`

`P = {2, 3, 5, 7, 11}`

`O uu P = {1, 2, 3, 5, 7, 9, 11}`

Elements that are only in both sets can be identified using an intersect, which is shown with the #`nn`# symbol. Using the same sets, `O nn P` is a list of elements that are in O AND P:

`O nn P = {3, 5, 7, 11}`

which lists all the elements that can be found in both sets.

The number of elements in a set is shown as n(A), where A is the set for which the total is required.