# Definition: Set Union

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: ### Examples

1. 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.
2. 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.

Axioms: 1
Corollaries: 2
Definitions: 3 4 5 6 7 8 9 10 11
Explanations: 12 13
Lemmas: 14
Parts: 15
Proofs: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Propositions: 31 32 33 34 35 36 37
Theorems: 38

Github: ### References

#### Bibliography

1. Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
2. Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016