# Category:Class Union

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This category contains results about **Class Union**.

Definitions specific to this category can be found in Definitions/Class Union.

Let $A$ and $B$ be two classes.

The **(class) union** $A \cup B$ of $A$ and $B$ is defined as the class of all sets $x$ such that either $x \in A$ or $x \in B$ or both:

- $x \in A \cup B \iff x \in A \lor x \in B$

or:

- $A \cup B = \set {x: x \in A \lor x \in B}$

### General Definition

Let $A$ be a class.

The **union of $A$** is:

- $\bigcup A := \set {x: \exists y: x \in y \land y \in A}$

That is, the class of all elements of all elements of $A$ which are themselves sets.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Class Union"

The following 14 pages are in this category, out of 14 total.

### C

### U

- Union of Class is Transitive if Every Element is Transitive
- Union of Doubleton
- Union of Slow g-Tower is Well-Orderable
- Union of Slowly Well-Ordered Class under Subset Relation is Well-Orderable
- Union of Subclass is Subclass of Union of Class
- Union of Transitive Class is Transitive
- Union of Union of Relation is Union of Domain with Image
- Union with Superclass is Superclass