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Exercise 1720Combinatorics › Inclusion-exclusionL1Added 3 Nov 2026

Pairwise but not triple

#IE#triple#void

Statement

If ∣A∣=∣B∣=∣C∣=10|A|=|B|=|C|=10, ∣A∩B∣=∣A∩C∣=∣B∩C∣=3|A\cap B|=|A\cap C|=|B\cap C|=3, and A∩B∩C=∅A\cap B\cap C=\emptyset, compute ∣A∪B∪C∣|A\cup B\cup C|.

Hint

IE with triple intersection zero.

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Solution

IE. 30−9+0=2130-9+0=21.

Conclusion. ∣A∪B∪C∣=21|A\cup B\cup C|=21.