The General Equation in the Algebra of Logic

A set of propositions regarding n logical classes may be represented by a set of equations containing n unknowns. In the analytic processes of deduction (represented by the solution of the equations) we replace the n (possibly over-lapping) classes by a number (in general greater than n) of mutually exclusive classes the existence of which i s implied by the original n classes ; though in the simpler processes (where a few logical steps may be safely omitted) the amplification need not be explicit, and in expressing the final result the classes may be regrouped into the original n (or any other) classes.