Inclusion-Exclusion for Counting

Inclusion-Exclusion for Counting

## Formula

For two sets $$a$$ and $$b$$:

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

For three sets:

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

## Usage

- Used when different counting cases overlap and direct addition would cause overcounting.

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