Principle of Inclusion and Exclusion Formulae

In this class, We discuss the Principle of Inclusion and Exclusion Formulae

The reader should have prior knowledge of set theory basics. Click Here

Principle: Let A and B be two sets.

The number of elements in the union of two sets, A and B, is the sum of the number of elements in the sets minus the number of elements in the intersection.

Formulae for two sets

|A ∪ B| = |A| + |B| – |A ∩ B|

The below diagram shows an example.

Formulae for three sets.

|A ∪ B ∪ C| = |A| + |B| + |C| – |A ∩ B| – |A ∩ C| – |B ∩ C| + |A ∩ B ∩ C|

The diagram below shows the example