Inclusion–Exclusion Principle

A combinatorial rule that computes the cardinality of a finite union of (possibly overlapping) sets by alternately adding and subtracting the sizes of all nonempty intersections of those sets; classically expressed as a finite alternating sum over intersections of increasing order.

A combinatorial formula giving the cardinality of a finite union of sets as an alternating sum of the sizes of all nonempty intersections of those sets.