Inclusion–Exclusion in Counting

Add sizes of single sets, subtract pairwise intersections, add triples—sign alternates.

Try this in Python

def ie3(a, b, c, ab, ac, bc, abc):
    return a + b + c - ab - ac - bc + abc

print(ie3(10, 10, 10, 3, 3, 3, 1))

Key takeaways

• Ground sets must live in same universe.
• In code, bitmask positions often replace explicit sets.
• Stop at first nonzero layer if problem structure allows.