Cardinality of Set Operations

Cardinality of Set Operations

## Formula

$$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$

$$n(A-B)=n(A)-n(A\cap B)$$

$$n(B-A)=n(B)-n(A\cap B)$$

$$n(A\triangle B)=n(A)+n(B)-2n(A\cap B)$$

## Conditions / Special Cases

If:

$$A\cap B=\varnothing$$

then:

$$n(A\cup B)=n(A)+n(B)$$

If:

$$A\subseteq B$$

then:

$$n(B-A)=n(B)-n(A)$$

## Usage

- Used in counting problems involving overlapping sets, differences and symmetric differences.