The technique of compiling signal riddles and logical chains. Techniques for developing students' skills in building a logical chain of reasoning
Goals: train students in solving logical problems; develop logical and abstract thinking, memory, attention; form harmonious interpersonal relationships to cultivate respect for each other, to form the ability to cooperate.
Methodological comment : this activity can be done with children different ages, depending on their intellectual training; the teacher himself chooses the tasks for solving, the tasks about Inspector Varnik can be offered for staging.
Epigraphs:
Solving logical problems is the first step to the development of a child.
E.Davydova
Logic is the art of arriving at an unpredictable conclusion.
Samuel Johnson
Without logic, it is almost impossible to bring ingenious discoveries of intuition into our world.
Kirill Fandeev
A person who thinks logically stands out pleasantly against the background of the real world.
American saying
Logic is the morality of thought and speech.
Jan Lukasiewicz
Event progress
1. Teacher's word
Logic tasks , as well as mathematics, is called "mind gymnastics". But unlike mathematics,logic tasks - this is an entertaining gymnastics, which in a fun way allows you to test and train thought processes, sometimes in an unexpected perspective. To solve them, you need quick wit, sometimes intuition, but not special knowledge.Solving logic problems is to thoroughly analyze the condition of the problem, to unravel the tangle of contradictory connections between characters or objects.Logic tasks - these are, as a rule, whole stories with popular actors in which you just need to get used to, feel the situation, visualize it and catch the connections.
Even the mostdifficult logic puzzles do not contain numbers, vectors, functions. But the mathematical way of thinking is necessary here: the main thing is to comprehend and understand the conditionlogical task . The most obvious decision on the surface is not always the right one. But more often than not,solving a logic problem turns out to be much simpler than it seems at first glance, despite the confusing condition.
In the process of decisionlogic tasks you will get acquainted with mathematical logic - a separate science, otherwise called "mathematics without formulas." Logic as a science was created by Aristotle, who was not a mathematician, but a philosopher. And logic was originally part of philosophy, one of the methods of reasoning. In the work "Analytics" Aristotle created 20 schemes of reasoning, which he called syllogisms. One of his most famous syllogisms is: “Socrates is a man; all men are mortal; So Socrates is mortal. Logic (from other Greek.Λογική - speech, reasoning, thought) is the science of correct thinking, or, in other words, "the art of reasoning".
There are certain methodssolving logic problems :
way of reasoning , with the help of which the simplest logical problems are solved. This method is considered the most trivial. In the course of the solution, reasoning is used that consistently takes into account all the conditions of the problem, which gradually lead to a conclusion and the correct answer.
tables way, used in solving text logic problems. As the name implies, solving logical problems consists in building tables that allow you to visualize the condition of the problem, control the process of reasoning, and help draw the right logical conclusions.
graphs way consists in sorting out possible scenarios for the development of events and the final choice of the only correct solution.
flowchart method - a method widely used in programming and solving logical transfusion problems. It consists in the fact that, first, operations (commands) are allocated in the form of blocks, then the sequence of execution of these commands is established. This is the block diagram, which is essentially a program, the execution of which leads to the solution of the task.
billiard way follows from the theory of trajectories (one of the sections of probability theory). To solve the problem, it is necessary to draw a billiard table and interpret the actions of the movements of the billiard ball along different trajectories. It is necessary to keep records possible outcomes in a separate table.
Logic tasks can seem like tough nuts not only for children, but also for adults. Think carefully before posting an answer. For convenience, you can do the calculation on paper.
2. Presentation of commands
3. Problem solving.
The autocratic ruler of one island wanted to prevent aliens from settling on the island. Wanting to keep the appearance of justice, he issued an order according to which anyone who wants to settle on the island should, after thinking it over, make any statement, and after a preliminary warning that his life depends on the content of this statement. The order read: “If the stranger tells the truth, he will be shot. If he tells a lie, he will be hanged." Can an alien become a resident of the island?
To solve it, you need to make an assumption. That by "truth" we mean that the content of the alien's statement coincides with the decision of the ruler that preceded it (which the alien may not know). For example, the ruler could decide in advance that the stranger would be shot. If the stranger guesses this decision and says: “They will shoot me,” then the first part of the order will come into force. We further assume that the ruler will not change his decision under the influence of the alien's answer, and also that the ruler will always decide either to be shot or hanged. Let us designate the content of the statement (coincidence of the decision of the ruler and the statement of the stranger) by P if it is a hanging and by P if it is a shooting. Then you can create a table:
Obviously, if the stranger says: "I am condemned to hang", by this he will create a stalemate for the ruler: either the ruler will contradict his own order (first line), or his own decision (third line). Therefore, by the statement "I am condemned to hang" the stranger can save his life, of course, on the assumption that the ruler does not want to deviate from either his decision or his order.
According to the agreement, the procedure for approving a new project, in the development of which institutions A, B, C participate, is as follows: if A and B participate in the approval first, then institution C must also join the participation. If approval occurs first in institutions B and C, Institution A also joins. The question is: are there possible cases when approving a project, when only institutions A and C would take part in it, while the participation of institution B would not be necessary (while maintaining an agreement on the procedure for approving projects)?
Two tribes live on the island: well done. Who always tell the truth, and liars who always lie. The traveler met an islander, asked him who he was, and when he heard that he was from a tribe of fellows, he hired him as a guide. They went and saw another islander in the distance, and the traveler sent his guide to ask him what tribe he belonged to. The guide returned and said that he claims to be from a tribe of fellows. The question is: was the conductor a good fellow or a liar?
Before the court are three people, of which each can be either an aborigine or an alien. The judge knows that natives always answer questions truthfully, and aliens always lie. However, the judge does not know which of them is an aborigine and which is an alien. He asks the first one, but does not understand his answer. Therefore, he asks first the second, and then the third about what the first answered. The second says that the first said that he was an aborigine. The third says that the first called himself an alien. Who were the second and third defendants?
The second is an aborigine, the third is an alien.
The beetle went on a journey. He crawls along the tape, the length of which is 90 centimeters. At the other end of the ribbon, two centimeters from the end, is a flower. How many centimeters will the beetle have to crawl to the flower: 88 or 92 (provided that it crawls all the time on one side and only at the end can it cross over to the other side through the end of the tape)?
Marina took a long time choosing which jug to buy. Finally chose. The saleswoman put the purchase in a box. What did Marina buy? How many jugs did the saleswoman put on the shelves on which they stood before?
The tourist walked to the lake. He came to a crossroads, from where one road led to the right and the other to the left; one went to the lake, the other did not. Two guys were sitting at the crossroads, one of them always told the truth, the second always lied. Both of them answered any question with either "yes" or "no". All this was known to the tourist, but he did not know which of them was telling the truth and which was lying; he also did not know which road led to the lake. The tourist put only one question to one of the guys. What was the question, since he knew from the answer which road leads to the lake?
There were nine students left in the class during the break. One of them broke the window. The teacher's question was answered as follows:
Jacob. Jack did it.
Bean. It is not true.
Maria. I broke it.
John. Either Maria or Anna did it.
Jack. Bob is lying.
Volume. It was Maria.
Leo. No. Maria did not break the window.
Anna. Neither Mary nor I did.
Rosalia. Anna is right, but Jack is also innocent.
If three of these nine statements are true, and only three are true, who broke the window?
How many triangles can be counted in this figure (an uncolored drawing is given)?
Read carefully and do not write anything down: Torpedo tops the standings, Spartak is in fifth place, and Dynamo is right in the middle between them. If Lokomotiv is ahead of Spartak, and Zenit takes place immediately behind Dynamo, then which of the listed teams is in second place? You have 30 seconds to think.
The enterprise has three workshops - A, B, C, which have agreed on the procedure for approving projects, namely: 1. If workshop B does not participate in the approval of the project, then workshop A does not participate in this approval. 2. If workshop B participates in design approval, then shops A and C take part in it. The question is: under these conditions, is shop C obliged to take part in the approval of the project when shop A participates in the approval?
Shop C must participate in project approval if shop A is involved.
Which of these nine mustaches went on an "evening walk"?
a - 6, b - 8, c - 5
Which of the 7 buttons should be pressed. For the bell to ring? It is recommended to find the path mentally.
In the Moscow semi-finals of the European Basketball Championship, held in Soviet time, the places were distributed as follows: the USSR - 14 points, Italy and Czechoslovakia - 12 points each, Israel - 11, Finland - 10, East Germany and Romania - 9 points each and Hungary - 7 points. According to the position. Each team received 2 points for a win, 1 point for a loss, and 0 points for a no-show. Draws were not allowed. Make a summary table of the results of the games if it is known that the Finnish team won against the Italian team and lost to the Romanian team.
All teams had to play 28 games, that is, play 84 points. Since they scored 14 + 12 + 12 + 11 + 10 + 9 + 9 + 7 = 84 points, there were therefore no no-shows. Each team played 7 games. Maximum amount possible points - 14, minimum - 7. It is clear that the USSR team won all the matches, and the Hungarian team lost all the matches. The Italian team lost two games (to the teams of Finland and the USSR), therefore, won against the team of Czechoslovakia, which, in turn, lost to the teams of Italy and the USSR, and won all the other matches. Therefore, the Israeli team won against the teams of Finland, East Germany and Romania. Since the athletes of Romania outperformed the athletes of Finland, they consequently lost to the athletes of the GDR, who, in turn, lost to the athletes of Finland. The table has been compiled.
On Tuesday, at about 10 am, a stranger burst into Inspector Warnicke's room. He was extremely excited. His hands were trembling, his tousled hair stuck out in all directions. A few minutes later, after lighting a cigarette and calming down, the visitor began his story: - This morning I returned from vacation. All night I had to shake on the train. I didn't get enough sleep and when I got home I decided to lie down on the sofa. From fatigue, I did not immediately notice that the piano had disappeared from the room, and the coffee table and armchair had been moved. On this sheet of paper, I drew a plan for the arrangement of the furniture in the room before I left. - Here's what, dear, - said Inspector Varnicke, glancing briefly at the drawing, - First of all, it's quite clear to me that you didn't have a piano at all. Now let's find out why you needed this lie. Why did Inspector Varnicke doubt the veracity of the visitor's story?
The drawing that Inspector Varnicke saw shows the piano incorrectly. The figured notch at the piano is always on the right side.
It was time for the zoo to close. The last belated visitors had already begun to gradually move towards the exit, when suddenly an indignant cry was heard. One zoo visitor, a middle-aged lady, lost her elegant handbag. She even managed to see the back of the fleeing kidnapper. Immediately, Inspector Varnicke rushed after him, who never manages to spend even a few hours calmly. He was joined by one of the visitors who declared that he knew all the moves and exits here. Together they ran around the entire park. The perpetrator was nowhere to be found. He could not leave the territory of the park: only the central gate remained open, and by order of the inspector, the most careful observation was established behind them. Varnike had already wondered if his assistant was leading him by the nose. Maybe he is an accomplice of the kidnapper and is now trying to cover up the tracks? But immediately this thought left the inspector, for one circumstance, which suddenly attracted his attention, allowed him to discover the villain. What did the criminal reveal himself to be?
Inspector Varnicke drew attention to the "employee" of the zoo, who tried in vain to feed the rhinoceros with meat. Rhinos are known to be herbivores.
You are given 2 minutes to memorize the words shown in the picture. You can rewrite them. Then close the drawing and write from memory, as many words as you can remember. If you have written down less than fifteen words, we advise you to seriously train your attention and memory.
6 circles are divided into parts. You have half a minute to decide which two circles are divided into the largest number of parts. If you start doing calculations, you will not meet the allotted time. The only way out is to evaluate by eye.
There are five pairs of cubes in front of you. Look at them carefully. Find pairs in which the cubes are exactly the same. Time limit is two minutes.
Four teams participated in the ice hockey championship of the city, which was held according to the circular system (each team played once with each team): "North", "South", "East" and "West". According to the regulations, the team received two points for a win, one point for a draw and zero points for a loss. The last meeting ended unexpectedly: "North" lost to "East". However, this did not prevent the "North" from becoming a champion, and the "East" did not improve its standings in the tournament. How did the "East" and "West" play among themselves?
In total, 6 games were played and, therefore, 12 points were played. "North" has no more than 4 points, since it did not lose the last game. On the other hand, it cannot have 3 points, since otherwise each of the remaining teams has no more than 2 points (North took first place), and therefore all four teams have a total of no more than 3 + 2 + 2 + 2 = 9 points. Thus, "North" has 4 points, and he won against "South" and "West". Before last game"East" could not, obviously, have 2 points and even 1 point. Otherwise, having won against Sever, he would have risen higher in the standings. Consequently, the other two games "Vostok" lost, that is, he scored only 2 points. Therefore, the "South" and "West" won against the "East", and played a draw between themselves.
What is in the picture?
Imagine that you color the drawing as follows: the parts marked with a square are blue color, a cross - gray, a triangle - blue, a dot - brown, a vertical dash - black, a tick - green, a circle - yellow (the sun - too), two horizontal dashes - red. The unmarked parts will remain white. Now try to determine what is drawn in the picture without real coloring.
bank robbed
Bank robbed. Imagine for a moment that you are at the scene of an accident. Everything happened in 20 seconds (the time allotted for looking at the picture). Now try to help the investigation and answer a number of questions:
1. Do you remember the number of the car?
2. Was there a radio in the car?
3. Did the driver sit on the right or left?
4. Were there any dents or damage on the car, and if so, where?
5. How many robbers were there?
6. What headgear was the driver wearing?
7. Did you notice any special features of the bandit who was carrying the sack?
8. How many people stood on the steps?
9. Was there any particular damage to the building?
10. Who else witnessed the robbery?
Identical mugs
Of these 18 circles, only two are exactly the same. Find them.
Mugs numbered 4 and 14
points
Which of the cells, in your opinion, contains the most dots, and which one has the fewest? You have 10 seconds to think.
in the 8th
Three brothers
Three brothers, Ivan, Dmitry and Sergey, teach various disciplines at the universities of Moscow, St. Petersburg and Kyiv. Ivan does not work in Moscow, and Dmitry does not work in St. Petersburg. A Muscovite does not teach history. The one who works in St. Petersburg teaches chemistry. Dmitry does not teach biology. What discipline does Sergey teach, and at the university of which city?
52. The numbers in the second circle are obtained by dividing by two numbers inscribed in the first circle. The numbers in the third circle are obtained by doubling the numbers inscribed in the first circle.
Which figure is redundant?
Which of these figures is "extra"?
Figure number 5. The first and third figures make a pair. A pair is formed by the second figure with the fourth. In each pair, one of the figures is rotated by 90°, and the black and light parts of the figures are reversed. Figure 5 does not follow these patterns.
Antique glass theft
I absolutely cannot imagine, Mr. Inspector, who would need a glass of the 17th century, especially since it is impossible to sell it. - With these words, the director of the museum met Inspector Varnike. The glass was in place last night. Nobody came into the room after me. I locked it myself. The museum is cleaned by the Zeisigs, they have been working for us for a very long time and, of course, beyond all suspicion. “Yes, Herr Inspector, everything was in order during the evening cleaning,” said Herr Zeisig. Inspector Varnicke thought for a moment. - How long ago did you start collecting museum rarities? he suddenly asked Zeisig. What led Inspector Varnick to suspect the Zeisig family of stealing the glass?
The Zeisig family fell victim to a professional habit. The couple, having stolen a glass, removed the glass fragments of the display case.
A road accident
Mr. Inspector, I assure you that the misunderstanding occurred only due to my absent-mindedness. - Please don't worry. We are now listening to the victim. Please speak! - I was traveling with this gentleman in the same compartment. Even when landing, I noticed that both luggage nets were filled with various bundles. Only the place above this gentleman remained free, where I put my suitcase. On the way, we talked. I told him that I was going to my son, to whom I was taking as a gift albums with a very valuable collection of stamps, which I had been collecting for many years. Then I fell asleep and woke up when the train had already arrived at the place. Having dressed, I was about to leave, when I suddenly noticed that my suitcase was not where I had put it. I opened it and saw that it was filled with cotton toys. How glad I am that you managed to apprehend this scoundrel! How dare you accuse me of stealing! Take a closer look, because our suitcases are exactly the same, I just mixed them up. "And yet, I still have to detain you," said Inspector Varnicke. On what basis did Inspector Varnicke conclude that the misunderstanding did not occur by mistake?
It was impossible to mix up the suitcases: the difference in weight was too great.
The king called three heroes to the court. And he asks: - Who killed the Serpent Gorynych? Ilya Muromets said: - Dobrynya Nikitich killed the snake. Dobrynya Nikitich said: - Alyosha Popovich killed the snake. Alyosha Popovich said: - I killed the snake. Only one hero told the truth, the other two were cunning. So who killed the Serpent Gorynych?
Ilya Muromets said the truth: Dobrynya Nikitich killed the snake
Three sisters: Polly, Sarah and Ada. They came from the village to Big city study. One sister became a builder, one an architect, and a third a cook. Later, all the sisters got married. One husband was called Mr. Adamson, the second was simply Pedro, and the third was called Dr. Smith. No one in the families had the same first letters of the profession, the name of the husband and wife. (Sarah did not become a builder and her husband is not Smith). Pedro's wife is not a builder. What is the name of the doctor's wife?
Passengers are traveling in the Petersburg-Moscow passenger train. Sidorov, Petrov and Ivanov. The driver, electrician and conductor have the same surnames. Hints: - Ivanov lives in Moscow - The passenger, the conductor's namesake, lives in St. Petersburg - The conductor lives half way from St. Petersburg to Moscow - The passenger who is closer to the conductor's place of residence than other passengers - three times older than the conductor - 20 years old at that time Passenger Petrov turned one day - Sidorov (from the brigade) won billiards from an electrician. What is the driver's last name?
In the quiz, Mikhail was asked to choose one of the boxes. A prize is hidden in one of the boxes. Mikhail got 4 clues - a prize in a yellow or red box - a prize in a green or blue box - a prize in a green box - there is no prize in the yellow box Three clues are wrong, but only one is correct. Andrew thought and opened the right box. What colour?
Yellow
Four schoolchildren have the following names: Peter, Andrey, Fedor and Ivan. Surnames: Petrov, Andreev, Fedorov, Ivanov. None of them proper name and last name are not the same. Andreev's name is not Ivan. The name of a schoolboy with the surname Fedorov is the surname (almost) of a schoolboy whose name is the surname Peter.
The bank employs: manager, controller and cashier. Their names are: Boris, Ivan, Sasha. The cashier has no brothers, sisters, and he is the shortest of all. Sasha is married to Boris's sister and is taller than the controller. What is the name of the cashier, controller and manager?
There are 4 children in the family. The youngest is 5, the oldest is 15. The other two are 8 and 13 years old. Children's names: Borya, Galya, Vera and Anya. What is the age of each child if one girl goes to kindergarten. Anya is older than Boris. The sum of Anya's and Vera's years is divisible by 3.
Eight drawings group by two so that the following 4 combinations are formed: 1. Two identical fakirs and two identical snakes; 2. Two identical fakirs, but with different snakes; 3. Two different fakirs, but with the same snakes; 4. Two different fakirs with two different snakes.
4. Summing up. Winner's reward ceremony.
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Logical chain consists of metal signs "⇒" soldered together, symbolizing the cyclical nature of any philosophical reflections and reminding the hero that happiness is not in thoughts, but in actions. The amulet was produced in a limited edition by chance by the demiurges at the dawn of civilization and has since been repeatedly sold, pawned and forged. The original is distinguished by the heaviness, inflexibility and iron character of the material. But even handmade chains made of light metals and with serviceable joints are also in great demand. After all, the main thing is not the execution of a sign of attention, but the noble impulse itself, and therefore even a cheap imitation ancient artifact will bring good luck to the hero, as it will please his god.
Historical background
… And in order to understand the root cause of this consequence, it is necessary to turn to the origins. There was a time when intelligence was not yet valuable, and heroes did not understand the meaning of cause and effect. Therefore, absolutely everything that happened was attributed to the will of the great Random. Nowadays, every child knows that everything random is far from accidental, and it is quite natural that gods were wound up in Godville. But since fortune can always be seen in any regularity, regular rainbows, lightning and strange phrases from nowhere continued to be perceived by the heroes as a manifestation of chance. However, the gods reciprocated stupidly, which inevitably led to the formation of a vicious circle. Demiurges' attachment to polygons has been known since ancient times, and it was not a surprise that they decided to break this circle by subjecting Godville to carpet lightning. These emergency measures led to quite predictable consequences: the metal neck talismans of all the heroes were baked into inextricable logical chains, and the heroes themselves, having recovered from the blow, thought. When stupid thinks, do not expect anything good. This time, an idea was born in empty minds that it would be nice to have a reason to be damned from above. At least it's a hundred times better than being beaten for nothing, for nothing. And iron logic transformed the cause into an effect, and it led the heroes to the gods, and the first agreed to annoy the second, and the second to protect and punish the first, and, as another consequence, it was good. And in order to understand the root cause of this consequence, it is necessary
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- (Greek logike̅́) the science of acceptable ways of reasoning. The word "L." in its modern use is ambiguous, although not as rich in semantic shades as ancient Greek. logos from which it comes. In the spirit of tradition with the concept of L ... Great Soviet Encyclopedia
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The simplest logical circuits. Part 1: general information about logic circuits and simple logic modules
- Electronics for beginners
Greetings to all.
I decided to write a few articles about the simplest logical circuits.
This topic will be of interest to people who have little understanding of the algebra of logic and logical constructions, rather than to professionals and experts on this topic.
So, let's begin.
What is a combinational logic circuit?
This is a circuit capable of processing binary electrical signals. At each moment in time, the outgoing signals of the combinational logic circuit (CLC) depend solely on the incoming signals. Therefore, the same combination of input values corresponds to the same combination of output values.The characteristic of CLC is the lack of memory. That is, the signals that previously entered the circuit do not matter. (“The current moment is important,” one of the characters in the film “21” said.)
Mathematical model of the KLC
For a better understanding, analysis and representation of complex circuits, their somewhat simplified mathematical models are used.Most models do not take into account the interaction time of chain elements during the development of the CLC. Therefore, we will assume that the output signals of the circuit instantly respond to changes in the input signals. Also, instead of a time signal function x(t), which can change its essence depending on the technology used (for example, 0 and 5 volts in TTL; 0 and 3.1 volts in CMOS), we will use a logical function x, which can take values 0 and 1.
Description of the work of the KLC
The so-called truth table is used to describe the operation of the CLC. This table indicates the values of the output signals for certain values of the input signals. It might look like this:In the truth table, the values of each of the signals are arranged in columns, and the rows indicate the correspondences between the signals.
I will give an example of a logical problem that is solved using such a table.
Let's say we have a water tower. To create the necessary pressure in the pipeline system, in the tower all day long there must be some amount of water. But you can’t draw water into the tower all the time - it is not dimensionless, and electricity is not cheap. We need to create a controller that will turn on and off the water supply to the tower, depending on several indicators.
The picture shows several sensors:
X is the time of day, where 1 is day and 0 is night (electricity is cheaper at night);
Y and Z are humidity sensors, for them 1 is water, and 0 is dry.
W will control the valve, turning it on (1) and off (0) as needed.
The truth tables for this case will look like this:
A) we simply list all possible combinations of X, Y, and Z readings;
b) look at the most simple options: if both Y and Z are 0, then it means that there is no water at all, so W must be turned on, and it does not matter if it is night or day. If both Y and Z have a value of 1, then this means that the tank is full, respectively, W must be turned off;
c) now about economy: if Z=1 and Y=0, then the water level in the tank is between the two sensors. At the same time, if this happens at night (X=0), then it is worth taking water to the maximum (W=1), and during the day (X=1(- leave everything as it is (W=0);
d) no improbable anywhere: there is a chance that Y will have a value of 1 when Z=0. Then, logically, it would be necessary to send a message about a malfunction in the system, but we will simply show that this simply cannot be.
Simple logic modules
Consider the simplest CLCs: Not-1, And-2, and Or-2 modules.Not-1
This is the simplest KLC, with one input and one output. The function of this module is to output the inverse of the input. Since there is only one entrance, there are only two exit options:
And-2
This module is already a bit more complicated. It has two entrances and one exit. The function of the And-2 module is as follows: the output will be 1 only if both inputs are also 1:
Or-2
Now another module with two inputs and one output. Only now the output will be 1 if at least one of the inputs is 1:
To be continued.
One of these days I will write a few more articles - next in line are multiplexers, half- and full-adders, as well as all kinds of combinations of modules.Thank you for your attention.
Every day a person is faced with a mass of life tasks that need to be solved logically. This includes the correct construction of the work schedule, official moments and even personal life. It would seem that everything is quite simple: exclude unimportant details, focus on serious aspects, thereby correctly setting priorities. However, in practice, the situation requires some effort. You can develop logic on your own, without signing up for special courses. Let's consider all the nuances in more detail.
Logical thinking: what is it?
The concept of " logical thinking It is easier to explain if you break the phrase into “logic” and “thinking”. Let's try to figure it out together, highlighting the main thing.
Logics
The concept comes from the Greek “reasoning”, “thought”, “the art of reasoning correctly”, “the science of thinking”. Let's analyze the concept, taking as a basis the science of right thinking. It consists of several aspects, such as the laws, methods and forms of the human intellect, namely his thoughts.
Logic is needed in order to achieve truth in the process of reasoning. Thanks to active brain activity, a certain scheme is launched that leads a person to the end point. The result is taken not by intuition, but from previously acquired knowledge.
For this reason, logic is often referred to as a science that allows you to reach conclusions through many conclusions and their connection. The main task of logic is the generalization of the available fragments together. As a result, a person receives true knowledge regarding the subject of reflection.
Thinking
Thinking allows you to find a connection between aspects of reality. However, in order for the process to take place at the “correct” level, one must think objectively. That is, before the main tasks, it is important to put yourself at the center of the current process, and not to watch everything from the outside. Objective or logical thinking must obey the basic laws of logic.
Logical thinking
From the foregoing, we can conclude what "logical thinking" is. As a result of the thought process, a person applies the knowledge gained earlier. Then, by inference, they are processed. All structures are connected in a logical chain in order. Conclusions are not based on assumptions, but on clear evidence, facts, prudence, objectivity, general laws logic. Ultimately, on the basis of the existing premises, the truth is obtained.
Why develop logical thinking
It is human nature to process information through brainstorming. Simply put, all people think this is a completely natural process. Thinking allows you to build a chain of personal behavior, to make correct conclusions in any given situation, take action. Such aspects play important role in situations where a decision is urgently needed. Ultimately, the goal will be achieved through logical reasoning.
When you fully learn the art of analyzing information, issues will be resolved many times faster. Through the proper collection and processing of information, you can build long term about their own actions. Such aspects help people feel comfortable in any situation. You will calculate in advance the possible nuances, then immediately exclude them in your head by searching for a new solution. You always need to think logically, no matter if you are at work or at home.
The greatest minds of the world annually bring out new ways of developing logical thinking. Experienced business trainers politicians, psychologists - they all help people develop. The most relevant ways to achieve what you want are puzzles aimed at the manifestation of logic. Also effective are games, a set of exercises for objective thinking, reading scientific and fiction, studying foreign languages.
Method number 1. Reading
- Many people know that books allow you to gain wisdom, become a versatile and well-read person. However, success can only be achieved through artistic or scientific literature. It is in such publications that there is more knowledge than in numerous reference books.
- To develop logical thinking, read at least 10 sheets daily. At the same time, it is important to analyze each line, gradually accumulating information in your head. The brain has selective properties, so at a certain moment you will be able to retrieve the necessary information.
- In the process of reading, analyze the chapters, try to think logically from the very beginning. Make bets on how the book will end, how this or that character will act in a particular situation. A. Conan Doyle's book "Sherlock Holmes" is considered a world bestseller. The work helps to develop logical thinking and pass the evening in a pleasant company.
Method number 2. Games
- The most common games aimed at developing logical thinking are checkers and chess. In the process of rivalry, opponents calculate their actions many steps ahead. It is this move that allows you to win, nothing else. It is not difficult to learn tactics, it is enough to devote 2-3 hours daily to this business. As the age of technology leaves its mark on society, you can play on a computer, phone or tablet. At the same time, you will have access to the logic simulator around the clock, regardless of the place and other "live" rivals.
- The next most popular game is Scrabble. Many have heard about it since childhood. Linguistic trainer for people who have little vocabulary and slow logic. As a result of manipulations, you will learn how to compose words from existing letters, laying them out in a certain sequence. As in the previous case, you can play on a PC or smartphone. In addition to the development of logic, you will become more concentrated, attentive.
- To improve logical thinking, you can play with words. There are several variations of such an adventure, we will consider them in order. Some prefer to name one long word (the number of letters is from 10), after which the task of other participants is to compose other words from the “raw materials”. The one with the highest number wins. The second option is as follows: a person calls a word, the next one says another word, starting with the last letter of the previous one. For example, you said "sailor", the opponent answered "apartment".
- The World Wide Web is literally full of various banners that offer to go to the site from logical riddles. Such a move will allow developing thinking not only in adults, but also in children. Also popular games are crossword puzzles, sudoku, rebuses, reversi. Download applications on your smartphone that help develop logical thinking. Such a move will train the brain in public transport or in a traffic jam. This is much more useful than studying flyers and tired faces of people.
- Take a closer look at games like Rubik's Cube or backgammon, collect puzzles, play poker. Thanks to increased concentration, memory and logical thinking develop. The World Wide Web allows you to play without a second partner, which is an indisputable plus. You can solve the Rubik's Cube while resting between classes or during your lunch break. The main thing in any business is regularity. Perform simple manipulations daily to achieve maximum results.
Method number 3. Exercises
- Mathematical problems and logical chains from the school (institute) program will help you develop logic quickly enough. Find old textbooks and start manipulating. Perform the exercise daily for 30-60 minutes. It will be especially difficult for the humanities, for whom mathematics is a bone in the throat. An analogue is the search for analogies or deciphering anagrams.
- Consider an exercise that consists in orderly building words or phrases of the same topic. the main task is as follows: you need to build words from smallest to largest. That is, the first designation characterizes a specific species, and the last - a generalized concept. Let's take the word "violet" as an example. Violet - name - flower - plant. The more words you pick up and arrange them in one chain, the more logical thinking will be involved. The complex must be performed at least 2 times a day for 15 minutes.
- Another exercise is aimed not only at logical thinking, but also the development of intellectual abilities, attentiveness, observation, concentration and general perception. The main point is considered to be that you need to determine how correctly the conclusion is made. Is it logical, based on the connection between judgments.
For example: “Cats meow. Alice is a cat, so she can meow!” The judgment is logically correct. If we talk about the wrong logic, then it looks like this: “Woolen clothes are warm. Boots are also warm, so they are made of wool! An erroneous judgment, boots may not be made of wool, but their thermal qualities will exceed all expectations.
This exercise is often used by parents when working with children. It is important to ask your child to explain this or that conclusion. In this case, the child will quickly come to the desired conclusion.
Method number 4. Foreign language
- It is known that new information received activates brain activity, as a result of which all processes take place on the highest level. The sounds of foreign languages will make you think logically, make associations between native and foreign speech.
- Find an online course on the Internet or download video lessons, practice daily. Sign up for language school, learn thoroughly English, Spanish or even Chinese.
- The effect of the acquired knowledge will not keep you waiting. In addition, you will be able to travel around the countries, talking freely with local residents. Communicate in chats and forums with the inhabitants of Europe or America, develop the acquired knowledge.
It is difficult enough to develop logical thinking, but the procedure cannot be called unrealistic. Consider popular games such as backgammon, checkers, chess, poker. Decide math problems, build logical chains using electronic resources, learn foreign languages.
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