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
 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.
 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.
Table of Contents
 Proposition: Sets are Subsets of Their Union
 Proposition: Set Union is Commutative
 Proposition: Set Union is Associative
Mentioned in:
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
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References
Bibliography
 Reinhardt F., Soeder H.: "dtvAtlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
 Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016