Let $A$ and $B$ be sets. Based on the disjunction operation “\(\vee\)”, the set **union** of \(A\) and \(B\) is defined as \[A\cup B:=\{x | x\in A \vee x\in B\}.\]

The union is the set containing all elements \(x\) belonging either to \(A\) or to \(B\) (including those belonging to both). It can be visualized as the following Venn diagram:

- Let $A=\{1,2,3,4\}$ and let $B=\{3,4,5,6\}.$ Then the set union is $A\cup B=\{1,2,3,4,5,6\}$. Please note that we do not have to list the repeating elements twice in the union set.
- The union of the set of countries of Europe and the set of the countries of Asia equals the set of the countries belonging to Eurasia.

| | | | | created: 2017-08-12 20:59:49 | modified: 2019-07-28 19:22:53 | by: *bookofproofs* | references: [979], [7838]

[7838] **Kohar, Richard**: “Basic Discrete Mathematics, Logic, Set Theory & Probability”, World Scientific, 2016

[979] **Reinhardt F., Soeder H.**: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10