定理
$$\left| S_{1}\cup S_{2}\ldots \cup S_{n}\right|$$
$$=\sum_{i} |S_i| - \sum_{i<j} |S_{i_1}\cap S_{i_2}| + \sum_{i<j<k} |S_{i_1}\cap S_{i_2}\cap S_{i_2}| + \dots + (-1)^{n-1}|S_{i_1}\cap S_{i_2}\cap \dots \cap S_{i_k}|$$
$$\left| S_{1}\cup S_{2}\ldots \cup S_{n}\right|$$
$$=\sum_{i} |S_i| - \sum_{i<j} |S_{i_1}\cap S_{i_2}| + \sum_{i<j<k} |S_{i_1}\cap S_{i_2}\cap S_{i_2}| + \dots + (-1)^{n-1}|S_{i_1}\cap S_{i_2}\cap \dots \cap S_{i_k}|$$
原文：https://www.cnblogs.com/zwfymqz/p/8232476.html