Difference of Sets

Difference of Sets

## Definition / Concept

The difference $A-B$ contains elements that belong to $A$ but not to $B$.

## Formula

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

$$A-B=A\cap B'$$

## Conditions / Special Cases

In general:

$$A-B\ne B-A$$

If:

$$A\subseteq B$$

then:

$$A-B=\varnothing$$

If:

$$A\cap B=\varnothing$$

then:

$$A-B=A$$

$$B-A=B$$

## Usage

- Used when elements belonging to one set must be excluded from another set.