Rule of subtraction ($|A\setminus B|=|A|-|A\cap B|$)

For finite sets, removing the elements of $B$ from $A$ leaves $|A|-|A\cap B|$ elements. Indeed $A$ is the disjoint union of $A\setminus B$ and $A\cap B$, so the rule of sum proves the formula. If $B\subseteq A$, it reduces to $|A\setminus B|=|A|-|B|$.