 For any set "A", we define the disjoint complement to be the set formula_30.Disjoint complements are always bands, but the converse is not true in general.If "A" is a subset of "X" such that formula_31 exists, and if "B" is a subset lattice in "X" that is disjoint from "A", then "B" is a lattice disjoint from formula_32.