Union and Intersection

Union and Intersection

## Definition / Concept

The union contains elements belonging to at least one set, while the intersection contains elements common to both sets.

## Formula

$$A\cup B=\{x:x\in A\text{ or }x\in B\}$$

$$A\cap B=\{x:x\in A\text{ and }x\in B\}$$

## Conditions / Special Cases

For disjoint sets:

$$A\cap B=\varnothing$$

If:

$$A\subseteq B$$

then:

$$A\cup B=B$$

$$A\cap B=A$$

## Usage

- Used to combine sets or identify common elements.