This article focuses on solving the disjunctive problem. Various methods of constructing the disjunctive cuts (DC) from the logical limitations on the linear inequalities have been presented. A general principle of DC and a principle making possible to strengthen these cuts were stated. By virtue of the stated principles, solving the problems of optimization with a great number of limitations can be simplified. Two theorems were formulated and proved. Four examples illustrated various theoretical statements. The suggested principles and procedures on their basis provide the theoretical background to the elaboration of algorithms intended for the software implementation in solving the practical problems.