Sets

# Cardinality of sets

## In case of two sets

$A,B\subseteq \Omega$
$\left|A\cup B\right|=\left|A\right|+\left|B\right|-\left|A\cap B\right|$
$\left|\Omega \setminus \left(A\cup B\right)\right|=\left|\Omega \right|-\left|A\right|-\left|B\right|+\left|A\cap B\right|$

## In case of three sets

$A,B,C\subseteq \Omega$
$\left|A\cup B\cup C\right|=\left|A\right|+\left|B\right|+\left|C\right|-\left|A\cap B\right|-\left|A\cap C\right|-\left|B\cap C\right|+\left|A\cap B\cap C\right|$
$\left|\Omega \setminus \left(A\cup B\cup C\right)\right|=\left|\Omega \right|-\left|A\right|-\left|B\right|-\left|C\right|+\left|A\cap B\right|+\left|A\cap C\right|+\left|B\cap C\right|-\left|A\cap B\cap C\right|$