Universal Set and Complement

Universal Set and Complement

## Definition / Concept

The universal set $U$ contains all objects under consideration. The complement of $A$ contains all elements of $U$ that do not belong to $A$.

## Formula

$$A'=U-A$$

$$A'=\{x\in U:x\notin A\}$$

## Conditions / Special Cases

$$A\cup A'=U$$

$$A\cap A'=\varnothing$$

$$U'=\varnothing$$

$$\varnothing'=U$$

$$\left(A'\right)'=A$$

## Usage

- Used to represent exclusion and solve set problems involving complements.