Branches History Index

◀ ▲ ▶Branches / Set-theory / Definition: Set Union

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:

venn3

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.

Table of Contents

  1. Proposition: Sets are Subsets of Their Union
  2. Proposition: Set Union is Commutative
  3. 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

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs

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