Symmetric Difference

Symmetric Difference

## Definition / Concept

The symmetric difference contains elements that belong to exactly one of the two sets.

## Formula

$$A\triangle B=(A-B)\cup(B-A)$$

$$A\triangle B=(A\cup B)-(A\cap B)$$

## Conditions / Special Cases

$$A\triangle A=\varnothing$$

$$A\triangle\varnothing=A$$

$$A\triangle B=B\triangle A$$

## Usage

- Used when common elements must be excluded while retaining elements belonging to only one set.