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MATHEMATICAL SCIENCES
DIRECT APPLICATION OF IMPLICATION AND EQUIVALENCE
UDC 519.9
Nematov Islom
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of “Mathematics” of the Faculty of Mathematics and Computer Science of Fergana State University
Aliev Ibratjon Xatamovich
2nd year student of the Faculty of Mathematics and Computer Science of Fergana State University
Ferghana State University, Uzbekistan
Annotation. Discrete mathematics, which is increasingly gaining popularity, has also been able to find its own application thanks to the introduction of new information sciences using the binary number system, both in the face of classical and quantum computer science. In this paper, the question of finding not only the indirect, but also the direct direct application of implication and equivalence operations known since the 60s of the XX century, the search for which has continued to the present time, is considered.
Keywords: discrete mathematics, implication, equivalence, direct application, practical application, technical understanding, electrical circuit.
Аннотация. Дискретная математика всё больше получающая популярность также смогла найти и собственное применение благодаря введению новых информационных наук с использованием двоичной системы счисления, как в лице классической, так и квантовой информатики. В данной работе рассмотрен вопрос относительно нахождения не только известного ещё с 60-х годов XX века косвенного, но и непосредственного прямого применения операций импликации и эквиваленции, поиск коих продолжался до настоящего времени.
Ключевые слова: дискретная математика, импликация, эквиваленция, прямое применение, практическое применение, техническое осмысление, электрическая схема.
At the moment, a variety of operations are actively used in discrete mathematics and logic to describe the conduct of actions on judgments. So the main operations are conjunction, disjunction and negation, so known as logical multiplication, logical addition and logical negation, respectively. They allowed us to operate on various judgments that accept the result either “true” – 1 or “false” – 0.
Each of the operations at the same time had its own truth table. For conjunction it is (Table 1), for disjunction – (Table 2) and logical negation – (Table 3).
At the same time, for the conjunction (logical “And”), a serial connection scheme takes place in the practical description (Fig. 1), described in the following cases:
1. If there is no current through “A” and through “B”, as a result there is no current;
2. If there is a current in “A”, but in the absence through “B”, as a result there is no current;
3. If there is no current in “A”, but in the presence of “B”, as a result there is no current;
4. If there