The union of two sets and is the set which contains all and all , denoted . In the Venn diagram below, is the entire area shaded in blue.
We can extend this to any (finite or infinite) family , writing for the union of this family. Formally, for a family of sets:
Alternatively, and equivalently,
Often elements of sets are taken from some universe of elements under consideration (for example, the real numbers , or living things on the planet, or words in a particular book). When this is the case, it is meaningful to discuss the complement of a set: if is a set of elements from some universe , then the complement of is the set
where is the universe of
Here are some examples of set unions:
The first three of these are the union of disjoint sets, while the latter three are not - in those cases, the sets overlap each other.
|Date of creation||2013-03-22 12:14:19|
|Last modified on||2013-03-22 12:14:19|
|Last modified by||rm50 (10146)|