Solution of equations in Boolean algebra

The explicit form of solutions of Boolean equations with one unknown is obtained. The effectiveness of the method is demonstrated for a number of equations whose solution previously has been found only in “tabular” form. The proposed approach leads to a method for solving systems of equations in Boolean set algebra. We use it to analyze the famous paradoxes of set theory, such as the barber paradox and the liar paradox, as well as Russell's and Cantor's paradoxes. Translated from Nelineinaya Dinamika i Upravlenie, pp. 119–132, 1999.