\Big{|}A_1 \cup A_2 \cup \cdots \cup A_n \Big{|} = \sum_{1 \leq i \leq n} \Big{|}A_i \Big{|} - \sum_{1\leq i < j \leq n} \Big{|}A_i \cap A_j \Big{|} + \sum_{1\leq i < j < k \leq n} \Big{|}A_i \cap A_j \cap A_k \Big{|} + \cdots + (-1)^{n-1} \Big{|}A_1 \cap A_2 \cap \cdots \cap A_n \Big{|}