Essence and classification of economic relations
From the moment of his separation from the world of wild nature, man develops as a biosocial being. This determines the conditions for its development and formation. The main stimulus for the development of man and society is needs. To satisfy these needs, a person must work.
Labor is the conscious activity of a person to create goods in order to satisfy needs or obtain benefits.
The more the needs increased, the more complex the labor process became. It required ever greater expenditures of resources and ever more coordinated actions of all members of society. Thanks to work, both the main features of the external appearance of modern man and the characteristics of man as a social being were formed. Labor moved into the phase of economic activity.
Economic activity refers to human activity in the creation, redistribution, exchange and use of material and spiritual goods.
Economic activity involves the need to enter into some kind of relationship between all participants in this process. These relations are called economic.
Definition 1
Economic relations are the system of relationships between individuals and legal entities formed in the production process. redistribution, exchange and consumption of any goods.
These relationships have different forms and durations. Therefore, there are several options for their classification. It all depends on the criterion chosen. The criterion may be time, frequency (regularity), degree of benefit, characteristics of the participants in this relationship, etc. The most frequently mentioned types of economic relations are:
- international and domestic;
- mutually beneficial and discriminatory (benefiting one party and infringing on the interests of the other);
- voluntary and forced;
- stable regular and episodic (short-term);
- credit, financial and investment;
- purchase and sale relations;
- proprietary relations, etc.
In the process of economic activity, each of the participants in the relationship can act in several roles. Conventionally, three groups of carriers of economic relations are distinguished. These are:
- producers and consumers of economic goods;
- sellers and buyers of economic goods;
- owners and users of goods.
Sometimes a separate category of intermediaries is distinguished. But on the other hand, intermediaries simply exist in several forms at the same time. Therefore, the system of economic relations is characterized by a wide variety of forms and manifestations.
There is another classification of economic relations. The criterion is the characteristics of the ongoing processes and goals of each type of relationship. These types are the organization of labor activity, the organization of economic activity and the management of economic activity.
The basis for the formation of economic relations of all levels and types is the right of ownership of resources and means of production. They determine the ownership of the goods produced. The next system-forming factor is the principles of distribution of produced goods. These two points formed the basis for the formation of types of economic systems.
Functions of organizational and economic relations
Definition 2
Organizational-economic relations are relationships to create conditions for the most efficient use of resources and reduce costs through the organization of forms of production.
The function of this form of economic relations is the maximum use of relative economic advantages and the rational use of obvious opportunities. The main forms of organizational and economic relations include concentration (consolidation) of production, combination (combination of production from different industries in one enterprise), specialization and cooperation (to increase productivity). The formation of territorial production complexes is considered the completed form of organizational and economic relations. An additional economic effect is obtained due to the favorable territorial location of enterprises and the rational use of infrastructure.
Soviet Russian economists and economic geographers in the middle of the twentieth century developed the theory of energy production cycles (EPC). They proposed organizing production processes in a certain area in such a way as to use a single flow of raw materials and energy to produce a whole range of products. This would dramatically reduce production costs and reduce production waste. Organizational and economic relations are directly related to economic management.
Functions of socio-economic relations
Definition 3
Socio-economic relations are the relations between economic agents, which are based on property rights.
Property is a system of relations between people, manifested in their attitude towards things - the right to dispose of them.
The function of socio-economic relations is to streamline property relations in accordance with the norms of a given society. After all, legal relations are built, on the one hand, on the basis of property rights, and on the other, on the basis of volitional property relations. These interactions between the two parties take the form of both moral norms and legislative (legally enshrined) norms.
Socio-economic relations depend on the social formation in which they develop. They serve the interests of the ruling class in that particular society. Socio-economic relations ensure the transfer of ownership from one person to another (exchange, purchase and sale, etc.).
Functions of international economic relations
International economic relations perform the function of coordinating the economic activities of countries around the world. They bear the character of all three main forms of economic relations - economic management, organizational-economic and socio-economic. This is especially relevant nowadays due to the variety of models of a mixed economic system.
The organizational and economic side of international relations is responsible for expanding international cooperation based on integration processes. The socio-economic aspect of international relations is the desire for a general increase in the level of well-being of the population of all countries of the world and a reduction in social tension in the world economy. Management of the global economy is aimed at reducing contradictions between national economies and reducing the impact of global inflation and crisis phenomena.
function ". Let's start with a special but important case of functions acting from to .If we understand what a relation is, then understanding what a function is is quite simple. A function is a special case of a relation. Every function is a relation, but not every relation is a function. What relations are functions? What additional condition must be met for a relation to be a function?
Let's return to the consideration of the relation operating from the domain of definition to the domain of values. Consider an element from . This element corresponds to an element such that the pair belongs to , which is often written in the form: (for example, ). The relation may also contain other pairs, the first element of which may be the element . This situation is not possible for functions.
A function is a relation in which an element from the domain of definition corresponds to a single element from the domain of values.
The relation “having a brother”, presented in Fig. 1, is not a function. Two arcs go from a point in the domain of definition to different points in the domain of values, therefore this relation is not a function. Content-wise, Elena has two brothers, so there is no one-to-one correspondence between the element from and the element from.
If we consider the relation “to have an older brother” on the same sets, then such a relation is a function. Each person can have many brothers, but only one of them is the elder brother. Functions include such family relationships as “father” and “mother”.
Usually, when talking about functions, the letter , and not, as in the case of relations, is used to generally designate a function, and the general notation has the usual form: .
Consider the well-known function 
. The domain of definition of this function is the entire real axis: 
. The range of values of the function is a closed interval on the real axis: 
. The graph of this function is a sinusoid; each point on the axis corresponds to a single point on the graph .
One-to-one function
Let the relation define the function. What can be said about the reverse relationship? Is it also a function? Not at all necessary. Let's look at examples of relations that are functions.
For the relation “has an older brother,” the inverse relation is the relation “has a brother or sister.” Of course, this relationship is not a function. An older brother may have many sisters and brothers.
For the "father" and "mother" relationships, the inverse relationship is the "son or daughter" relationship, which is also not a function, since there can be many children.
If we consider the function 
, then the inverse relation 
is not a function, since one value corresponds to as many values as desired. To consider
As for the functions (from the Latin Functio - execution, implementation) of communication, they are understood as the external manifestation of the properties of communication, the roles and tasks that it performs in the process of an individual’s life in society.
There are various approaches to the classification of communication functions. Some researchers consider communication in the context of its organic unity with the life of society as a whole and with direct contacts of people and the inner spiritual life of a person.
The listed functions, taking into account their integral nature, are those factors that show a significantly more significant role of communication for a person than simply transmitting information. And knowledge of these integral functions that communication performs in the process of individual human development makes it possible to identify the causes of deviations, disruptions in the interaction process, defective structure and form of communication in which a person has been involved throughout his life. The inadequacy of a person’s forms of communication in the past significantly affects his personal development and determines the problems that confront him today.
The following functions are distinguished:
communication is a form of existence and manifestation of human essence, it plays a communicative and connecting role in the collective activities of people;
represents the most important vital need of a person, a condition for his prosperous existence, has a psychotherapeutic, confirmatory meaning (confirmation of one’s own “I” by another person) in the life of an individual of any age.
A significant part of researchers highlight the functions of communication related to the exchange of information, interaction and perception of each other by people.
Thus, B. Lomov identifies three functions in communication: information-communicative (consists in any exchange of information), regulatory-communicative (regulation of behavior and regulation of joint activities in the process of interaction, and affective-communicative (regulation of the emotional sphere of a person.
The information and communication function covers the processes of generating, transmitting and receiving information; its implementation has several levels: at the first level, differences in the initial awareness of people who come into psychological contact are equalized; the second level involves the transfer of information and decision-making (here communication realizes the goals of information, training, etc.); the third level is associated with a person’s desire to understand others (communication aimed at forming assessments of achieved results).
The second function - regulatory-communicative - is to regulate behavior. Thanks to communication, a person regulates not only his own behavior, but also the behavior of other people, and reacts to their actions, that is, a process of mutual adjustment of actions occurs.
Under such conditions, phenomena characteristic of joint activity appear, in particular, the compatibility of people, their teamwork, mutual stimulation and correction of behavior. This function is performed by such phenomena as imitation, suggestion, etc.
The third function - affective-communicative - characterizes the emotional sphere of a person, in which the individual’s attitude to the environment, including social, is revealed.
You can give another, slightly similar to the previous, classification - a four-element model (A. Rean), in which communication forms: cognitive-informational (reception and transmission of information), regulatory-behavioral (focuses attention on the characteristics of the behavior of subjects, on the mutual regulation of their actions ), affective-empathic (describes communication as a process of exchange and regulation at the emotional level) and social-perceptual components (the process of mutual perception, understanding and cognition of subjects).
A number of researchers are trying to expand the number of communication functions by clarifying them. In particular, A. Brudny distinguishes the instrumental function necessary for the exchange of information in the process of management and collaboration; syndicative, which is reflected in the cohesion of small and large groups; translational, necessary for training, transfer of knowledge, methods of activity, evaluation criteria; function of self-expression, focused on searching and achieving mutual understanding.
L. Karpenko, according to the “goal of communication” criterion, identifies eight more functions that are implemented in any interaction process and ensure the achievement of certain goals in it:
contact - establishing contact as a state of mutual readiness to receive and transmit messages and maintain communication during interaction in the form of constant mutual orientation;
informational - exchange of messages (information, opinions, decisions, plans, states), i.e. reception - transmission of what data in response to a request received from a partner;
incentive - stimulating the activity of the communication partner, which directs him to perform certain actions;
coordination - mutual orientation and coordination of actions to organize joint activities;
understanding - not only adequate perception and understanding of the essence of the message, but also the partners’ understanding of each other;
amotivational - inducing the necessary emotional experiences and states from a communication partner, changing one’s own experiences and states with his help;
establishing relationships - awareness and fixation of one’s place in the system of role, status, business, interpersonal and other connections in which the individual will act;
implementation of influence - a change in the state, behavior, personal and meaningful formations of the partner (aspirations, opinions, decisions, actions, activity needs, norms and standards of behavior, etc.).
Among the functions of communication, scientists also highlight social ones. The main one is related to the management of social and labor processes, the other is related to the establishment of human relations.
The formation of a community is another function of communication, which is aimed at supporting socio-psychological unity in groups and is associated with communicative activities (the essence of the activity is in creating and maintaining a specific relationship between people in groups); it allows for the information exchange of knowledge, relationships and feelings between people, i.e. .e. has the goal of transmitting and perceiving social experience by the individual. Among the social functions of communication, the functions of imitation of experience and personality change are important (the latter is carried out on the basis of mechanisms of perception, imitation, persuasion, infection).
Studying the specifics of socio-political activity allows us to identify the following main functions of communication in this area of knowledge (A. Derkach, N. Kuzmina):
Socio-psychological reflection. Communication arises as a result and as a form of conscious reflection by partners of the peculiarities of the course of interaction. The socio-psychological nature of this reflection is manifested in the fact that, first of all, through linguistic and other forms of signaling, elements of the interaction situation, perceived and processed by an individual, become really valid for his partners. Communication becomes less an exchange of information and more a process of joint interaction and influence. Depending on the nature of this mutual influence, coordination, clarification, mutual complementation of the substantive and quantitative aspects of the “individual” display occurs with the formation of group thought, as a form of collective thinking of people, or, conversely, a clash of opinions, their neutralization, containment, as happens in interpersonal conflicts and inadequate mutual influences (cessation of communication);
Regulatory. In the process of communication, direct or indirect influence is exerted on a group member in order to change or maintain at the same level his behavior, actions, state, general activity, characteristics of perception, value system and relationships. The regulatory function allows you to organize joint actions, plan and coordinate, coordinate and optimize group interaction of team members. Regulation of behavior and activity is the goal of interpersonal communication as a component of objective activity and its final result. It is the implementation of this important function of communication that allows us to evaluate the effect of communication, its productivity or unproductivity;
Cognitive. The named function is that as a result of systematic contacts in the course of joint activities, group members acquire various knowledge about themselves, their friends, and ways to most rationally solve the tasks assigned to them. Mastering the relevant skills and abilities, it is possible to compensate for insufficient knowledge of individual group members and their achievement of the necessary mutual understanding is ensured precisely by the cognitive function of communication in combination with the function of socio-psychological reflection;
Expressive. Various forms of verbal and nonverbal communication are indicators of the emotional state and experience of a group member, often contrary to the logic and requirements of joint activity. This is a kind of manifestation of one’s attitude to what is happening through an appeal to another member of the group. Sometimes a discrepancy in the methods of emotional regulation can lead to alienation of partners, disruption of their interpersonal relationships and even conflicts;
Social control. Methods for solving problems, certain forms of behavior, emotional reactions and relationships are normative in nature; their regulation through group and social norms ensures the necessary integrity and organization of the team, the consistency of joint actions. Various forms of social control are used to maintain consistency and organization in group activities. Interpersonal communication mainly acts as negative (condemnation) or positive (approval) sanctions. It should be noted, however, that not only approval or condemnation is perceived by participants in joint activities as punishment or reward. Often, the lack of communication can be perceived as one or another sanction;
Socialization. This function is one of the most important in the work of the subjects of activity. By engaging in joint activities and communication, group members master communication skills, which allows them to interact effectively with other people. Although the ability to quickly assess an interlocutor, navigate situations of communication and interaction, listen and speak play an important role in a person’s interpersonal adaptation, the ability to act in the interests of the group, a friendly, interested and patient attitude towards other group members are even more important.
An analysis of the features of communication in the field of business relationships also indicates its multifunctionality (A. Panfilova, E. Rudensky):
the instrumental function characterizes communication as a social control mechanism, which makes it possible to receive and transmit information necessary to carry out a certain action, make a decision, etc.;
integrative - used as a means of uniting business partners for a joint communication process;
the function of self-expression helps to assert oneself, demonstrate personal intelligence and psychological potential;
broadcast - serves to convey specific methods of activity, assessments, opinions, etc.;
the function of social control is designed to regulate the behavior, activities, and sometimes (when it comes to trade secrets) the language actions of participants in business interaction;
the socialization function contributes to the development of business communication culture skills; With the help of the expressive function, business partners try to express and understand each other’s emotional experiences.
V. Panferov believes that the main functions of communication are often characterized without resorting to an analysis of the functions of a person as a subject of interaction with other people in joint life activities, which leads to the loss of the objective basis for their classification. Analyzing the classification of communication functions proposed by B. Lomov, the researcher poses the question: “Are the series of functions exhaustive in terms of their number? How many such rows can there be? What main classification can we talk about? How are the different bases related to each other?
Taking this opportunity, let us recall that B. Lomov identified two series of communication functions with different bases. The first of them includes three classes of already known functions - information-communicative, regulatory-communicative and affective-communicative, and the second (according to a different system of bases) - covers the organization of joint activities, people’s knowledge of each other, the formation and development of interpersonal relationships.
Answering the first question posed, V. Panferov identifies six among the main functions of communication: communicative, informational, cognitive (cognitive), emotive (that which causes emotional experiences), conative (regulation, coordination of interaction), creative (transformative).
All of the above functions are transformed into one main function of communication - regulatory, which manifests itself in the interaction of an individual with other people. And in this sense, communication is a mechanism of social-psychological regulation of people’s behavior in their joint activities. The identified functions, according to the researcher, should be considered as one of the grounds for classifying all other functions of a person as a subject of communication.
Exercises.
1) Using the Newton binomial formula at a = 1, b = i calculate +++…, +++…, +++…, +++…
2) Using the Moivre formula, calculate verbally sin 4j And cos 5j .
Lecture 3.
- CONFORMITY. FUNCTIONS. RELATIONSHIP. EQUIVALENCE RELATIONSHIP
Definition. We will say that on the set X given binary relation R, If " x, y О X we can determine (by some rule) where these elements are in relation R or not.
Let us define the concept of relationship more strictly.
Let's introduce the concept Cartesian (direct) product A´B arbitrary sets A And B.
A-priory A´B = ( (a, b), a О A , bО B). The Cartesian product of 3, 4 and an arbitrary number of sets is defined similarly. A-priory A´A´ …´A = A n .
Definitions.
1. Compliance S from many A into the multitude B called a subset S Í A´B. The fact that the elements aО A, bО B are in accordance S, we will write it in the form (a, b) О S or in the form aSb.
2. Naturally for correspondences S 1 And S 2 are determined S 1 ∩S 2 And S 1 U S 2– as the intersection and union of subsets. As for any subsets, the concept of inclusion of correspondences is defined S 1 Í S 2. So S 1 Í S 2 Û
from a S 1 b Þ a S 2 b.
3. For matches S 1 Í A´B And S 2 Í B´C let's define composition correspondences S 1 *S 2 Í A´С. We will assume that for the elements aО A, сО С a-priory a S 1 *S 2 s Û $ bО B such that a S 1 b And b S 2 s.
4. For compliance S Í A´B let's determine the correspondence
S -1 Í B´A so: by definition bS -1 a Û a S b.
5. Let, by definition, correspondence D A Í A´A,
D A =((a,a), aО A).
6. Compliance F from many A into the multitude B called function, defined on A, with values in B(or display from A V B), If " aÎ A $! bÎ B such that aFb. In this case we will also write aF = b or, more commonly, Fa = b. In this definition, a function is identified with its graph. In our notation aF 1 *F 2 s can be written in the form c = (aF 1)F 2. Composition F 2 F 1 functions means by definition that (F 2 F 1)(a)= F 2 (F 1 (a)). Thus, F 2 F 1 = F 1 * F 2 .
7. For display F from A V B way subsets A 1 Í A
called a subset F(A 1)= (F(a)| aО A 1 ) Н B, A prototype subsets B 1 Í B called a subset
F -1 (B 1)= ( aÎ A | F(a) Î B 1 ) Í A .
8. Display F from A V B called injection, if from
a 1 ¹ a 2 Þ Fa 1 ¹ Fa 2.
9. Display F from A V B called surjection, If
" bО B $ aО A such that Fa = b.
10. Display F from A V B called bijection or one-to-one mapping, If F– injection and surjection at the same time.
11. A bijection of a finite (and sometimes infinite) set is called substitution.
12. Binary relation on a set X called a subset R Í X´X. The fact that the elements x, y О X are in a relationship R, we will write it in the form (x, y) О R or in the form xRy.
Display f of a set X into a set Y is considered given if each element x of X is associated with exactly one element y of Y, denoted f(x).
The set X is called domain of definition mapping f, and the set Y is range of values. Set of ordered pairs
Г f = ((x, y) | x∈X, y∈Y, y = f(x))
called display graph f. It follows directly from the definition that the graph of f is a subset of the Cartesian product X×Y:
Strictly speaking, a map is a triple of sets (X, Y, G) such that G⊂ X×Y, and each element x of X is the first element of exactly one pair (x, y) of G. Denoting the second element of such a pair by f(x), we obtain a mapping f of the set X into the set Y. Moreover, G=Г f. If y=f(x), we will write f:x→y and say that element x goes or maps to element y; the element f(x) is called the image of the element x with respect to the mapping f. To denote mappings we will use notations of the form f: X→Y.
Let f: X→Y be a mapping from set X to set Y, and A and B are subsets of sets X and Y, respectively. The set f(A)=(y| y=f(x) for some x∈A) is called way set A. Set f − 1 (B)=(x| f(x) ∈B)
called prototype set B. A mapping f: A→Y such that x→f(x) for all x∈A is called narrowing mapping f to the set A; the narrowing will be denoted by f| A.
Let there be mappings f: X→Y and g: Y→Z. The mapping X→Z under which x goes to g(f(x)) is called composition mappings f and g and is denoted by fg.
A mapping of a set X into X, in which each element goes into itself, x→x, is called identical and is denoted by id X .
For an arbitrary mapping f: X→Y we have id X ⋅f = f⋅id Y .
The mapping f: X→Y is called injective, if for any elements from and it follows that . The mapping f: X→Y is called surjective, if every element y from Y is the image of some element x from X, that is, f(x)=y. The mapping f: X→Y is called bijective, if it is both injective and surjective. The bijective map f: X→Y is invertible. This means that there is a mapping g: Y→X called reverse to a map f such that g(f(x))=x and f(g(y))=y for any x∈X, y∈Y. The inverse of f is denoted by f − 1 .
The invertible mapping f: X→Y sets one-to-one correspondence between elements of the sets X and Y. The injective mapping f: X→Y establishes a one-to-one correspondence between the set X and the set f(X).
Examples. 1) The function f:R→R >0, f (x)=e x, establishes a one-to-one correspondence between the set of all real numbers R and the set of positive real numbers R >0. The inverse of the mapping f is the mapping g:R >0 →R, g(x)=ln x.
2) The mapping f:R→R ≥ 0, f(x)=x 2, the set of all real R onto the set of non-negative numbers R ≥ 0 is surjective, but not injective, and therefore is not bijective.
Function properties:
1. The composition of two functions is a function, i.e. if , then .
2. The composition of two bijective functions is a bijective function, if , then .
3. A mapping has an inverse mapping then and
if and only if f is a bijection, i.e. if , then .
Definition. n – local relation, or n – local predicate P, on the sets A 1 ; A 2 ;…; And n is any subset of the Cartesian product.
Designation n - local relation P(x 1 ;x 2 ;…;x n). When n=1 the relation P is called unary and is a subset of the set A 1 . Binary(binary for n=2) relation is a set of ordered pairs.
Definition. For any set A, the relation is called the identical relation, or diagonal, and - the complete relation, or the complete square.
Let P be some binary relation. Then domain of definition of a binary relation P is called a set for some y), and range of values– a set for some x). Reverse a set is called a relation to P.
The relation P is called reflective, if it contains all pairs of the form (x,x) for any x from X. The relation P is called anti-reflective, if it does not contain any pairs of the form (x,x). For example, the relation x≤y is reflexive, and the relation x The relation P is called symmetrical, if along with each pair (x,y) it also contains a pair (y,x). The symmetry of the relationship P means that P = P –1. The relation P is called antisymmetric, if (x;y) and (y;x), then x=y. The relation R is called transitive, if, together with any pairs (x,y) and (y,z), it also contains the pair (x,z), that is, from xPy and yPz follows xPz. Properties of binary relations: Example. Let A=(x/x – Arabic numeral); Р=((x;y)/x,yA,x-y=5). Find D;R;P -1 . Solution. The relation P can be written in the form P=((5;0);(6;1);(7;2);(8;3);(9;4)), then for it we have D=(5;6 ;7;8;9); E=(0;1;2;3;4); P -1 =((0;5);(1;6);(2;7);(3;8);(4;9)). Consider two finite sets and a binary relation. Let us introduce the matrix of the binary relation P as follows: . The matrix of any binary relation has properties: 1. If and , then , and the addition of matrix elements is carried out according to the rules 0+0=0; 1+1=1; 1+0=0+1=1, and multiplication is termwise in the usual way, i.e. according to the rules 1*0=0*1=0; 1*1=1. 2. If , then , and the matrices are multiplied according to the usual rule for matrix multiplication, but the product and sum of elements when multiplying matrices is found according to the rules of step 1. 4. If , then and Example. The binary relation is shown in Fig. 2. Its matrix has the form . Solution. Let, then; Let P be a binary relation on the set A, . The relation P on the set A is called reflective, if , where asterisks indicate zeros or ones. The relation P is called irreflexive, If . The relation P on the set A is called symmetrical, if for and for it follows from the condition that . It means that . The relation P is called antisymmetric, if it follows from the conditions that x=y, i.e. or . This property leads to the fact that all elements of the matrix outside the main diagonal will be zero (there can also be zeros on the main diagonal). The relation P is called transitive, if from and it follows that , i.e. . Example. The relation P and . Here on the main diagonal of the matrix are all units, therefore, P is reflexive. The matrix is asymmetrical, then the ratio P is asymmetrical Because not all elements located outside the main diagonal are zero, then the relation P is not antisymmetric. Those. , therefore the relation P is intransitive. A reflexive, symmetrical and transitive relation is called equivalence relation. It is customary to use the symbol ~ to denote equivalence relations. The conditions of reflexivity, symmetry and transitivity can be written as follows: Example. 1) Let X be a set of functions defined on the entire number line. We will assume that the functions f and g are related by the relation ~ if they take the same values at point 0, that is, f(x)~g(x), if f(0)=g(0). For example, sinx~x, e x ~cosx. The relation ~ is reflexive (f(0)=f(0) for any function f(x)); symmetrically (from f(0)=g(0) it follows that g(0)=f(0)); transitive (if f(0)=g(0) and g(0)=h(0), then f(0)=h(0)). Therefore, ~ is an equivalence relation. 2) Let ~ be a relation on the set of natural numbers such that x~y, if x and y give the same remainder when divided by 5. For example, 6~11, 2~7, 1~6. It is easy to see that this relation is reflexive, symmetrical and transitive and, therefore, is an equivalence relation. Partial order relation A binary relation on a set is called if it is reflexive, antisymmetric, transitive, i.e. 1. - reflexivity; 2. - antisymmetry; 3. - transitivity. A relationship of strict order A binary relation on a set is called if it is anti-reflexive, antisymmetric, transitive. Both of these relationships are called order relations. A set on which an order relation is specified, can be: a completely ordered set or partially ordered. Partial order is important in cases where we want to somehow characterize precedence, i.e. decide under what conditions to consider one element of the set to be superior to another. A partially ordered set is called linearly ordered, if there are no incomparable elements in it, i.e. one of the conditions or is satisfied. For example, sets with a natural order on them are linearly ordered.