A characterization of DeMorgan algebras

In this note we show that every de Morgan algebra is isomorphic to a two-subset algebra, 〈P,⊔,⊓,∼, 0P, 1P 〉, where P is a set of pairs (X,Y) of subsets of a set I, (X,Y)⊔(X ′, Y ′) = (X∩X ′, Y ∪Y ′), (X,Y)⊓(X ′, Y ′) = (X ∪ X ′, Y ∩ Y ′), ∼ (X,Y) = (Y,X), 1P = (∅, I), and 0P = (I, ∅). This characterization generalizes a previous result that applied only to a special type of de Morgan algebras called ternary algebras.