De Morgan's Laws

De Morgan's Laws

## Formula

$$(A\cup B)'=A'\cap B'$$

$$(A\cap B)'=A'\cup B'$$

For three sets:

$$(A\cup B\cup C)'=A'\cap B'\cap C'$$

$$(A\cap B\cap C)'=A'\cup B'\cup C'$$

## Conditions / Special Cases

The complement is taken with respect to the same universal set $U$.

## Usage

- Used to simplify complements of unions and intersections.

- Useful for converting set expressions into equivalent forms.