⚖️ Inclusion-Exclusion

Set counting problem

Calculate the union of multiple sets while avoiding overcounting.

Theory:

To count the union of two sets $A$ and $B$, the inclusion-exclusion principle is applied as:

$$|A\cup B|=|A|+|B|-|A\cap B|$$

For three sets, the formula is:

$$|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|B\cap C|-|A\cap C|+|A\cap B\cap C|$$

This formula ensures that no elements are counted multiple times.