Consider a Boolean algebra of subsets b(A) generated by a set A, which is the set of subsets of A that can be obtained by means of a finite number of the set operations union, intersection, and complementation. Then each of the elements of b(A) is called a Boolean function generated by A. Each Boolean function has a unique representation (up to order) as a union of complete products. It follows that there are 2^(2^p) inequivalent Boolean functions for a set A with cardinality p.

antichain | Boolean algebra | Booleans | complete product | conjunction | Dedekind's problem | Karnaugh map | mincut | monotonic function

BooleanFunction

George Boole | Richard Dedekind