Sets

## Sets

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.

## Example 1

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}

## Example 2

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}