If AAA and BBB are finite sets, what is the inclusion-exclusion principle for ∣A∪B∪C∣|A \cup B \cup C|∣A∪B∪C∣?
∣A∣+∣B∣+∣C∣−(∣A∩B∣+∣A∩C∣+∣B∩C∣)+∣A∩B∩C∣|A|+|B|+|C| - (|A \cap B| + |A \cap C| + |B \cap C|) + |A \cap B \cap C|∣A∣+∣B∣+∣C∣−(∣A∩B∣+∣A∩C∣+∣B∩C∣)+∣A∩B∩C∣
∣A∣+∣B∣+∣C∣−(∣A∩B∣+∣A∩C∣+∣B∩C∣)−∣A∩B∩C∣|A|+|B|+|C| - (|A \cap B| + |A \cap C| + |B \cap C|) - |A \cap B \cap C|∣A∣+∣B∣+∣C∣−(∣A∩B∣+∣A∩C∣+∣B∩C∣)−∣A∩B∩C∣
∣A∣+∣B∣+∣C∣+∣A∩B∣+∣A∩C∣+∣B∩C∣+∣A∩B∩C∣|A|+|B|+|C| + |A \cap B| + |A \cap C| + |B \cap C| + |A \cap B \cap C|∣A∣+∣B∣+∣C∣+∣A∩B∣+∣A∩C∣+∣B∩C∣+∣A∩B∩C∣
∣A∣+∣B∣+∣C∣−∣A∩B∩C∣|A|+|B|+|C| - |A \cap B \cap C|∣A∣+∣B∣+∣C∣−∣A∩B∩C∣