Boolean equations in algebra of logic and set theory (Q5947810)

The author considers the equation of one variable of the form \[ f(x, y_1, y_2,\dots,y_k) = 0, \tag{1} \] where the arguments \(x\) and \(\{y_i\}_{i=1}^k\) of the function \(f\) may take values from the set \(E_2= \{0;1\}\) and the function \[ f: E_2^{k+1} \to E_2 \] is a Boolean function. It is proved that any solution of the equation (1) can be represented by a disjunctive development on so-called basic solutions. Four examples of application of the method proposed for solving equations of Boolean algebra and set theory are presented.