Inclusion-Exclusion Principle — Venn Diagrams & Counting

🔢 Inclusion-Exclusion

The inclusion-exclusion principle counts elements in the union of sets by alternately adding and subtracting intersection sizes to avoid double-counting.

2 sets: |A∪B| = |A|+|B|−|A∩B|
3 sets: |A∪B∪C| = |A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C|

⚙ Mode

Region sizes

A only 15 B only 12 A∩B 8

🔭 View

📊 Results

|A∪B[∪C]|

Neither (N=100)

Largest set

A=23

Smallest ∩

A∩B=8