A set X is an unordered collection of objects, which are called the elements of X. For example, the three languages French, Russian and Chinese form a set, which we denote as X = {French, Russian, Chinese} (or equivalently, {Chinese, French, Russian} as order does not matter).

#### Subset (or cluster)

A set Y is a subset of a set X if every element in Y is also contained in X. For example, {French, Russian} is a subset of the set {French, Russian, Chinese}. Sometimes a subset of a set which contains at least one element is also known as a cluster.

#### Set union

The union of two sets X and Y, denoted X U Y is the set formed by taking all of the elements in X and all elements in Y. For example, {French, German} U {Italian, Russian, English} = {French, German, Italian, Russian, English}

#### Set intersection

The intersection of two sets X and Y, denoted XY, is the set formed by taking all those elements that are in both X and Y. For example, {French, German} ∩ {Italian, Russian, French} = {French}.

#### Empty set

The empty set is the set that contains no elements, which is usually denoted Ø.

#### Disjoint sets

Two sets are called disjoint if their intersection is the empty set, that is, they have no elements in common. So, for example, the two sets {French, German} and {Italian, Russian, English} are disjoint sets as their intersection is the empty set, i.e. {French, German} ∩ {Italian, Russian, English} = Ø.

#### Complement of a set

If Y is a subset of a set X then the complement of Y in X, denoted by X-Y, comprises of all those elements in X that are not in Y. For example, the complement of {French, Chinese} in the set {French, Chinese, Russian, Italian} is {Russian, Italian}.