A_1,A_2,\cdots,A_n에 대해, 다음 식이 성립한다.\displaystyle |A_1 \cup A_2 \cup \cdots \cup A_n|=\sum_{1\le i \le n}|A_i|-\sum_{1\le i<j \le n}|A_i\cap A_j| + \sum_{1\le i<j<k \le n}|A_i\cap A_j \cap A_k| +\cdots+(-1)^{n+1}|A_1\cap A_2\cap \cdots \cap A_n|
\displaystyle \left\vert\bigcup_{i=1}^n A_i\right\vert=\sum_{k=1}^n(-1)^{k+1}\left( \sum_{1\le i_1 < <\cdots < i_k\le n}| A_{i_1}\cap\cdots\cap A_{i_k}|\right)