Laws of Set Algebra

Laws of Set Algebra

## Formula

### Commutative Laws

$$A\cup B=B\cup A$$

$$A\cap B=B\cap A$$

### Associative Laws

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

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

### Distributive Laws

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

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

### Identity Laws

$$A\cup\varnothing=A$$

$$A\cap U=A$$

### Domination Laws

$$A\cup U=U$$

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

### Idempotent Laws

$$A\cup A=A$$

$$A\cap A=A$$

### Complement Laws

$$A\cup A'=U$$

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

### Absorption Laws

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

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

## Usage

- Used to simplify set expressions and prove equality between sets.