Definition

$∣ ⋃_{i = 1}^{n} A_{i} ∣ = \sum_{i = 1}^{n} ∣ A_{i} ∣ - \sum_{1 \leq i < j \leq n} ∣ A_{i} \cap A_{j} ∣ + \sum_{1 \leq i < j < k \leq n} ∣ A_{i} \cap A_{j} \cap A_{k} ∣ - \dots + (- 1)^{n + 1} ∣ A_{1} \cap \dots \cap A_{n} ∣$