Analytic solutions of logic equations (Q1904815)

The author deals with a system of disjunctive equations of the matrix form \(X = (A \& X) \vee B\), where \(A = |a_{ij} |\), \(X = \left( \begin{smallmatrix} x_1 \\ \vdots \\ x_n \end{smallmatrix} \right)\), \(B = \left( \begin{smallmatrix} b_1 \\ \vdots \\ b_n \end{smallmatrix} \right)\), \(i,j = 1, \dots, n\), and \(a_{ij}, x_i, b_i \in \{0,1\}\). The analytic solution of this system is formulated analogous to Cramer's rule for linear equations over fields.