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.

The number of cards in a suit of playing cards are defined as a universal set, such that

`xi = {2, 3, 4, 5, 6, 7, 8, 9 and 10}`.

Set E contains all the even numbers. Write out the members of that set.

Only the even numbers are required. The curly brackets define the set.

Answer: E = {2, 4, 6, 8, 10}

The number cards in one suit of a set of playing cards are defined as a universal set, such that `xi = {2, 3, 4, 5, 6, 7, 8, 9 and 10}`.

Set E contains all the even numbers. Set T contains all the numbers that are a multiple of 3.

List the elements in `E nn T`.

`E = {2, 4, 6, 8, 10}` and `T = {3, 6, 9}`

`E nn T ` is E intersection T: values have to be in both sets

`E nn T = {6}`

Answer: `E nn T = {6}`

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).