Boolean sets and most general solutions of Boolean equations

The aim of this paper is twofold. First we determine the most general form of the subsumptive general solution of a Boolean equation (Theorem 1 and Theorem 2). Then we discuss several characterizations of Boolean sets, meaning sets of zeros of Boolean functions, and prove that every Boolean transformation X=Φ(T)X=Φ(T) is the parametric general solution of a certain Boolean equation.