Last updates: 2 July 2011
DeMorgan's Laws. Let and be sets.
|Let be a set. Show that the set of all subsets of with operations union, intersection and complement is a Boolean algebra.|
These notes are an updated version of notes of Arun Ram from 1994.
A Boolean algebra is a complemented distributive lattice. References for Boolean algebras are [Brk, Chapt X] and [St, &Sect;3.4]. In particular, see the conditions for the finite Boolean algebra found in [St, p. 107-108].
[Brk] G.D. Birkhoff, Lattice Theory, ?????
[St] R.P. Stanley, Enumerative combinatorics, Vol. 1, ????
[Ram] A. Ram, Notes in abstract algebra, University of Wisconsin, Madison 1993-1994.