1. Determine which of the following sentences are logical statements and which are not (explain why):
- a) “The sun is a satellite of the earth”;
- b) “2+3 ´ 4 ”;
- v) “great weather today”;
- G) “in the novel by L.N. Tolstoy "War and Peace" 3 432 536 words”;
- e) “Saint Petersburg is located on the Neva”;
- e) “Bach's music is too complicated”;
- g) “the first space speed is 7.8 km / s”;
- h) “iron - metal”;
- and) “if one corner in a triangle is straight, then the triangle will be obtuse”;
- To) “if the sum of the squares of the two sides of the triangle is equal to the square of the third, then it is rectangular”.
2.
Indicate which of the statements in the previous exercise are true, which are false, and which are among those difficult or impossible to establish.
Answer
True: e), h), j);
false: a), i);
the truth is difficult to establish: G);
can be considered both true and false depending on the required accuracy of representation: g).
3. Give examples of true and false statements:
- a)from arithmetic; b) from physics;
- v)from biology; G) from computer science;
- e)from geometry; e) from life.
Answer Samples.
True statements: a) “2+2=4
”; b) "The force of attraction of bodies is inversely proportional to the square of the distance between them" v) "Hares eat plants"; G) "Bit is a fundamental unit of information used in information theory"; e) "Two triangles are equal if two sides and the angle between them of one triangle are equal to two sides and the angle between them of another triangle"; e) “Monday is the first day of the week.
4. Formulate the negatives of the following statements or expressions:
- a) “Elbrus - the highest mountain peak in Europe”;
- b) “2>=5 ”;
- v) “10<7 ”;
- G) “all natural numbers are integers”;
- e) “you can draw a circle through any three points on the plane”;
- e) “tennis player Kafelnikov did not lose the final game”;
- g) “”;
- h) “this morning is clear and warm”;
- and) “number n is divisible by 2 or 3”;
- To) “”;
- l) "on the test, each student wrote with his own pen".
Answer a) "Elbrus is not the highest mountain peak in Europe"; b) “2<5” ; v) “10>=7” ; G) "Not all natural numbers are integers"; e) "Not through any three points on the plane you can draw a circle"; e) "Tennis player Kafelnikov lost the final game"; g) “Target is not hit by the first shot”; h) "This morning is not clear or it is not warm"(Explanation. Let A = "This morning is clear", a B = "This morning is warm"... Then "This morning is clear and warm" can be written as AV, the negation of which is, which corresponds to the expression form “This morning is not clear or it is not warm”; and)"The number n is not divisible by 2 and it is divisible by 3"; To) "This triangle is not isosceles or it is not right-angled"; l)"Not every student wrote the control with his own pen"(option: "someone did not write the test with their own pen").
5. Determine which of the statements (expression forms) in the following pairs are negations of each other, and which are not:
- a) “5<10 ”, “5>10 ”;
- b) “10>9 ”, “10<=9 ”;
- v) “target hit by first shot”, “target hit with second shot”;
- G) “the car stopped at each of the two traffic lights”, “the car did not stop at each of the two traffic lights”,
- e) “mankind knows all the planets of the solar system”, “there are planets in the solar system unknown to mankind”;
- e) “there are white elephants”, “all elephants are gray”;
- g) “whale - mammal”, “whale - fish”;
- h) “it is not true that point A does not lie on line a”, “point A lies on line a”;
- and) “line a is parallel to line b”, “line a perpendicular to line b”;
- To) “this triangle is isosceles and right-angled”, “this triangle is not isosceles or it is not right-angled”.
Answer They are negations of each other: b), d), e), j);
are not negations of each other: a), c), f), g), h), i).
6. Determine the truth values of the statements:
- a) “having a certificate of secondary education is enough to enter the institute”;
- b) “the presence of a certificate of secondary education is necessary for admission to the institute”;
- v) “if an integer is divisible by 6, then it is divisible by 3”;
- G) “the similarity of triangles is a necessary condition for their equality”;
- e) “the similarity of triangles is a necessary and sufficient condition for their equality”;
- e) “triangles are similar only if they are equal”;
- g) “triangles are equal only if they are similar”;
- h) “equality of triangles is a sufficient condition for their similarity”;
- and) “for the triangles to be unequal, it is enough for them to be dissimilar”;
- To) “for a quadrilateral to be a square, it is enough that its diagonals are equal and perpendicular”.
7. Substitute statements in the following statement forms instead of logical variables a, b, c, d such that the compound statements obtained in this way have meaning in everyday life:
- a) if(a or(b and with)), then d;
- b) if (not a and not b), then(with or d);
- v)(a or b) if and only if(with and not d).
9. Formalize the warning a woman of ancient Athens gave to her son about to get involved in political activities: “ If you tell the truth, people will hate you. If you lie, the gods will hate you. But you have to tell the truth or lie. So people will hate you or gods will hate you”.
Also formalize the son's answer: “ If I speak the truth, the gods will love me. If I lie, then people will love me. But I have to tell the truth or lie. Means, gods will love me or people will love me”.
Answer
Solution. Let us introduce the notation for logical statements: a - "You will speak the truth"; b - "People will hate you"; c - "The gods will hate you"... We agree to consider that some given statement x true unless otherwise specified. Then the mother's warning can be written like this:. And the son's answer is:
a) "This morning is clear and warm"; |
g) "This morning is not clear or warm"; |
b) "This morning is clear and not warm"; |
h) "This morning is not clear and not warm"; |
v) "This morning is not clear and it is not warm"; |
and) "This morning is clear or not warm"; |
G) "This morning is not clear or it is warm"; |
To) "If it is three clear, then it is not warm"; |
e) "Is this morning clear or not warm"; |
l) "If this morning is not clear, then it is warm"; |
e) "This morning is not clear or not warm"; |
m) "This morning is clear and not warm". |
11. From the two given statements a and b, construct a compound statement that would be:
- a)true if and only if both given statements are false;
- b)false if and only if both given statements are true.
12. From the three given statements a, b, c, construct a compound statement that is true when any one of these statements is true, and only in this case.
Answer: .
13. Determine using truth tables which of the following formulas are identically true or identically false:
a) |
e) |
b) |
e) |
v) |
g) |
G) |
14. Simplify the following formulas using the laws of bonding:
Answer a) b c; b) a; v) c (a v b) v a b (Hint: repeat the fourth logical term 3 times); G) a v c.
15. Simplify the following formulas using the laws of absorption:
16. Build truth tables for logical formulas and simplify formulas using the laws of logic algebra:
- a)
- b)
- v)
- e)
- e)
- g)
- h)
- and)
- To)
17. Give examples of switching circuits containing at least two switches whose conductance function is
- a)identically equal to one;
- b)is identically zero.
18. Find the conduction functions of the following switching circuits:
a) |
b) |
||
v) |
G) |
19. Check the equivalence of the following switching circuits:
- a)
- b)
- v)
- G)
- e)
Answer
Equivalent: b), c), e);
are not equivalent: a), d).
Explanations. Let us denote the conductance functions of the considered switching circuits as F 1 and F 2, respectively. Then:
a) ;
;
b) ;
;
v) ;
;
e) ;
.
20. Build switching circuits with given conductance functions:
The first of the interviewed witnesses told the traffic police that they were Zhiguli, the first digit of the car's number is one. The second witness said that the car was of the Moskvich brand, and the number began with a seven. The third witness stated that the car was foreign, the license plate did not start with one. Upon further investigation, it turned out that each of the witnesses correctly indicated either only the make of the car, or only the first digit of the number. What brand was the car and what number did the number begin with?
Answer "Zhiguli", number starts with seven.
25.
Five classmates: Irena, Timur, Camilla, Eldar and Zalim became the winners of the Olympiads for schoolchildren in physics, mathematics, computer science, literature and geography.
It is known that:
- the winner of the Olympiad in informatics teaches Irene and Timur to work on a computer;
- Camilla and Eldar also became interested in computer science;
- Timur was always afraid of physics;
- Camilla, Timur and the winner of the Literature Olympiad are swimming; 26. Irena loves ice cream sundaes. The cafe had a choice of the following options:
- ice cream with nuts;
- ice cream with bananas;
- ice cream with blueberries;
- chocolate with blueberries;
- chocolate with strawberries.
In four versions, Irene did not like either the type of ice cream or the filling, and in one version she did not like either the ice cream or the filling. She asked to prepare a portion according to her taste from the available products.
Sundae with strawberries. Explanation. Two other possible options - chocolate with nuts and chocolate with bananas - do not fit according to the problem statement (the number of options in which both the type of ice cream and the filling are not liked, in these cases is equal to two instead of one).
What kind of ice cream and with what kind of fruit does Irena like?
Answer27. At the next stage of Formula 1 racing, the first four places were taken by Schumacher, Alesi, Hill and Coolhardt. The TV reporter who arrived late for the awarding ceremony managed to photograph the pilots who took the second and third places, who poured champagne on each other. At this time, Schumacher and the fourth rider were shaking hands. Then wet Hill came into the picture, congratulating the pilot who took second place. Finally, the operator filmed a scene in which Schumacher and Coulhardt tried to drag the fourth-placed pilot onto the podium. Looking through the footage, the director of the sports episode quickly figured out which of the pilots took which place. He knew that, in accordance with the ceremony of awarding the winners of the races, the pilots who took the first three places, poured champagne on each other from huge bottles of the famous company - the sponsor of the competition. What place did each pilot take?
Answer Schumacher came in first, Coolhardt came in second, Hill came in third and Alesi came in fourth. Explanation. Schumacher is not fourth, since he shook hands with the fourth; he is neither second nor third, since the pilots who took these places poured champagne on each other while he was shaking hands. Hence, Schumacher is the first. Further, since Hill is wet, then he took one of the prizes, but not the first and not the second (he congratulated the pilot who took the second place). Hence, Hill is third. Coulhardt did not come in fourth as he dragged the fourth-placed pilot onto the podium. Therefore, he is the second.28. In a certain kingdom-state, the Serpent Gorynych got into the habit of plundering. The king sent four heroes to destroy the Serpent, and he promised a great reward. The heroes returned with victory and the king asks them: "So which of you is the main winner, who will get the king's daughter and half the kingdom?" The good fellows were embarrassed and the answers were vague: Ilya Muromets said: “This is all Alyosha Popovich, the tsar-father”. Alyosha Popovich objected: "That was Mikula Selyaninovich." Mikula Selyaninovich: “Alyosha is not right, it’s not me”. Dobrynya Nikitich: "And not me, father." Baba Yaga turned up and said to the king: "But only one of the heroes is right, I saw the whole battle with my own eyes."
Which of the heroes defeated the Serpent Gorynych? thirty. Discussing the design of the new three-engined aircraft, the three designers in turn made the following assumptions:
1) if the second engine fails, you must land, and if the third engine fails, you can continue the flight;
2) if the first engine fails, you can fly, or if the third engine fails, you cannot fly;
3) if the third engine fails, you can fly, but if at least one of the others fails, you must sit down.
Flight tests have confirmed the correctness of each of the designers. Determine which engine fails to continue the flight.
Answer If the second engine fails, the flight cannot be continued.31. Andrey, Victor, Sasha and Dima took part in the swimming competition. Their friends speculated about possible winners:
1) Sasha will be the first, Victor will be the second;
2) Sasha will be the second, Dima will be the third;
3) Andrey will be the second, Dima will be the fourth.
At the end of the competition, it turned out that in each of the assumptions only one of the statements is true, the other is false.
What place in the competition did each of the young men take if they all took different places.
Answer The first place was taken by Sasha, the second - Andrey, the third - Dima, the fourth - Victor.32. For a long-term international expedition to a near-earth space station, it is necessary to select six specialists from eight applicants: in aeronautics, space navigation, biomechanics, energy, medicine and astrophysics. The flight conditions do not allow combining jobs in different specialties, although some applicants own two specialties. The duties of an aeronaut may be performed by Guerreti and Nam; space navigator - Clark and Frisch; biomechanics - Frisch and Nam; energy - Depardieu and Leonov; the doctor - Depardieu and Jorges; astrophysics - Volkov and Leonov.
According to the peculiarities of psychological compatibility, doctors recommend joint flights of Frisch and Clark, as well as Leonov with Jorges and Depardieu. On the contrary, it is undesirable for Depardieu to be on the same expedition with Nam, and Volkov with Clark. Who should be included in the expedition?
Answer The expedition should include: aeronaut - Guerreti, cosmonaut - Clark, biomechanic - Frisch, power engineer - Depardieu, doctor - Horches, astrophysicist - Leonov.
PEASANT WAR IN GERMANY
1. The program of Thomas Munzer and his supporters.
2. "Twelve Articles":
a) the general nature of this program;
b) its radical and moderate demands.
3. Burgers program:
a) a plan for political transformations in the empire;
b) the requirements of the townspeople;
c) the position of burghers in relation to chivalry.
MUNZER ABOUT FEODALS
Look, the main reason for usury, theft and robbery is our gentlemen and princes! They grab whatever they want: a fish in the water, a bird in the air, plants on the ground - everything should belong to them. And after that they [princes] spread God's commandments among the poor and say: God commanded - do not steal! But for themselves, they do not consider this prohibition mandatory. Therefore, they oppress all people, ruin and rob poor farmers, artisans and the whole world. If someone takes even a little from them, then he is sent to the gallows, and Dr. Lugner then says: "Amen!" The gentlemen are to blame for the poor man becoming their enemy. They do not want to eliminate the causes of indignation, how can they hope for peaceful well-being? That's what I say! Speeches like this call me a rebel. Let it go!
MUNZER ON FEDERAL EXPLOITATION AND FIGHT WITH FEDERALS
The meekest godfather Leisetreter ["Slow-moving"] claims that I wanted to raise an uprising, having subtracted it from my message to the miner. He talks about this, but is silent about the most important thing, about what I clearly stated to the princes. I announced to them that the power of the sword belongs to the whole community, as well as the key to absolution, and that on the basis of the text of Daniel (7), the Apocalypse (7) and the letter to the Romans (13.1), the princes are not masters, but the servants of the community. ... They should not act as they please, but according to justice ...
When, by what commandment did God give the princes such power that we, the poor, should spend all good days in the corvee and can work in our fields only in the rain, drenched in bloody sweat? In his justice, God will not tolerate that we are constantly forced to mow their meadows, cultivate arable land, sow, pull out, clean, crush, wash, ruffle, scratch and spin flax, peel peas, collect carrots and asparagus ... The curse of their shameful power and robber rights! What to say about those tyrants and villains who appropriate to themselves all taxes, duties and fees and shamelessly squander them, while they should go to the general treasury and benefit the whole country? If someone decides to grimace at this, they immediately act with him as with a traitor: they lead him to torture, chop off his head, and quarter. He is spared less than a mad dog ... Yes, their power is not from God, they are companions of the devil, their ruler is Satan. To overthrow this Moab and Behemoth is a truly godly deed; Scripture calls them not servants of God, but snakes and wolves ...
If until now you paid poll taxes and were serfs, now you will become "Real slaves, deprived of any right over yourself and your good. You will be sold, like in Turkey, like cattle, horses and oxen ... Woe, trouble to your children, to whom you will leave such an unfortunate legacy!
Read also:
|
1. I have a gift, a talent for understanding people, no one can deny this (___)
2. I will definitely help you to change yourself. (___)
3. Together with you we will try to see your problems with different eyes. (___)
4. Who would have thought that such a young and beautiful woman would think about death. (___)
5. You are serious about what is happening to you. (___)
6. You can count on my professional knowledge and experience. (___)
7. It is difficult to get started with so much resistance on your part. (___)
8. You would feel sorry for yourself, the faster you tell the truth, the easier we will find a solution. (___)
9. I think that my colleague will cope with this task more effectively. (___)
10. You are already disappointed! How? (___)
11. You definitely need to check with a psychiatrist. (___)
12. You should go to the mirror every day and say to yourself: "I am smart, I am beautiful, I am happy." (___)
13. I believe that it is extremely important for you to change your appearance. (___)
14. You now look like a prickly hedgehog, I think that you yourself do not really like it. (___)
15. Stop the hysterics, shut up! (___)
16. I think that you will agree with me, you need to take the following ... (___)
17. Most likely you should not engage in self-criticism, but self-study. (___)
19. You cannot repeat this endlessly - this is not a session of black magic. (___)
20. You need to choose for yourself new ways of expressing feelings for him. (___)
21. I'm going to give you a few options, but it's up to you to choose. (___)
22. I know that you will make the right decision for yourself. You have every reason for this. (___)
23. You have all the data to make the right decision and understand its consequences. (___)
24. Why don't you do it now? (___)
25. I want to offer you this option, maybe it will suit you ... (___)
26. No one will do it for you, do it yourself, you and you yourself will do it ... (___) ( According to G.S. Abramova)
Task number 26. Below are the most famous psychological recommendations. Do you think it is possible to use it in psychological counseling as a universal recommendation and why? Identify a significant flaw in this kind of recommendation. Give reasons for your answer.
1. P. Bragg offers a list of “commandments”: “The biggest sin is fear! The best day is today!<…>The biggest weakness is hatred.<…>The biggest need is a sense of community. The greatest thought is God. The greatest wealth is health.<…>The greatest friend and companion is good books.<…>Your enemies are envy, greed, self-indulgence, self-pity.<…>The smartest person is the one who always does what he thinks. This is the rule that you can follow to become an intelligent person. "
2. D. Carnegie proposes to be guided by 6 rules to always please people: 1) be sincerely interested in other people; 2) smile; 3) remember that a person's name is the sweetest sound most important to him in any language; 4) be a good listener, encourage others to talk about themselves; 5) talk about what interests your interlocutor; 6) instill in your interlocutor the awareness of his importance and do it sincerely.
Task number 27. From the following roles of a counselor psychologist, select those that are most often actualized in modern practice by professional (PP) and non-professional (NP) psychologists. Which roles do you think are more effective than others, and why?
Patient listener (___); "Vest" in which to cry (___); smart analyst (___); Suggestologist (___); expert in psychological laws (___); spiritual mentor (___); companion (___); "Healer of the soul" (___); advisor (___); Client's "second self" (___); a skilled facilitator for those who are discouraged (___); mediator (___), "arbitrator" (___).
2. ... Injuries do not heal overnight.
We act with the mind, not conjure
Just give me a time ...
(W. Shakespeare)
4. Power without abuse it loses its attractiveness. ( P. Valerie)
6. It is better to be absolutely wrong than to state the right things approximately correctly. ( J. Tukey)
8. Manage to catch the imp by the tail, and he will reveal to you where the devil is hiding. ( Chinese proverb)
11. A secret is something that you give to others to keep it. Confidence is what you had before you knew more about it. ( M. Alden)
13. Don't believe what you hear; do not trust traditions just because they are passed down from generation to generation; do not believe what is repeated by many; don't trust guesses ... Don't trust your masters and elders just because of their authority. When you are convinced by observation and analysis that the principle is consistent with the cause, that it leads to the benefit and well-being of all, accept it and hold on to it. ( Gautama Buddha)
14. Hundreds of people speak, but only one of them is able to think; thousands of people think, but only one of them is able to understand. A clear understanding is poetry, prophecy, and religion combined. ( J. Ruskin)
Semantic categories
Expressions (words and phrases) of a natural language that have any independent meaning can be divided into the so-called semantic categories, which include: 1) sentences: narrative, incentive, interrogative; 2) expressions that play a certain role in the composition of sentences: descriptive and logical terms 9.
Judgments are expressed in the form of declarative sentences (for example, "Kiev is a city", "A cow is a mammal"). In these judgments, the subjects, respectively, are "Kiev", "cow", and the predicates are "city", "mammal".
TO descriptive (descriptive) terms relate:
1. Item names- words or phrases denoting single (material or ideal) objects ("Aristotle", "first cosmonaut", "7") or classes of similar objects (for example, "steamer", "book", "poem", "drought", "Guards regiment", etc.).
In the judgment "Yenisei - the river of Siberia" there are three names of the subject: "Yenisei", "river", "Siberia". The name of the subject "Yenisei" plays the role of a subject, and the names "river" and "Siberia" are included in the predicate ("river of Siberia") as its two constituent parts.
2 Predictors- words and phrases denoting the properties of objects or relations between objects (for example, "decent", "blue", "electrically conductive", "there is a city", "less", "there is a number", "there is a planet", etc.). There are single and multiple predictors. Unary predictors denote properties (eg, "talented", "bitter", "great"). Multiple predictors denote (express) relationships. Double predictors are: "equal", "greater than", "mother", "remembers", etc. For example, "Land area A equal to the area of the land plot V","Maria Vasilievna - Seryozha's mother." An example of a triple predictor: "between" (for example, "The city of Moscow is located between the cities of St. Petersburg and Rostov-on-Don").
3. Functional signs- expressions denoting object functions, operations ("ctg α", "+", "V -", etc.).
In addition, the language contains the so-called logical terms(boolean constants, or boolean constants).
In natural language, there are words and phrases: "and", "or", "if ... then", "equivalent", "equivalent", "not", "it is not true that", "everyone" ("each", "All"), "some", "except", "only", "that ... which", "neither ... nor", "although ... but", "if and only
if ”and many others expressing logical constants (constants).
In symbolic (or mathematical) logic, conjunction, disjunction, negation, implication, equivalence, generality and existence quantifiers, and some others are usually used as such constants.
In symbolic logic, logical terms (logical constants) are expressed as follows:
Conjunction matches the conjunction "and". A conjunctive statement is denoted by, or, or (for example, “Lectures have ended (a), and the students went home (b) ").
Disjunction matches the conjunction "or". Disjunctive judgment is denoted by: (lax disjunction) and (strict disjunction); their difference is that with a strict disjunction, a complex judgment is true only if one of the constituent judgments is true, but not both, and with a weak disjunction, both judgments can be true at the same time. "He is a chess player or a football player" is indicated as "Now
Petrov is at home or at the institute "is denoted as
Implication corresponds to the conjunction "if ... then". A conditional judgment is indicated by: or (for example, "If the weather is good, we will go to the forest").
Equivalence matches the words "if and only if"
"If and only if", "equivalent". An equivalent statement is denoted by, or, or
Negation matches the words "not", "it is not true that". The denial of the statement is indicated (for example, "snow is falling" (a); "it is not true that snow is falling."
Community quantifier is denoted and corresponds to the quantum words "all" ("every", "every", "none"). - writing in mathematical logic (for example, in a judgment "Everything red fly agarics are poisonous "quantifier word" all ").
Existence quantifier denoted by 3 and corresponds to the words "some", "exists". -recording in mathematical logic (for example, in judgments "Some people have higher education "or ".Exists people who have higher education "(quantifiable words are in italics).
Let us express in the form of a diagram the varieties of semantic categories (Fig. 2).
1. Define descriptive and logical terms in the judgment: "All organisms are unicellular or multicellular." In this judgment, descriptive terms are: "organism", "multicellular organism", "unicellular organism", and logical terms: "all", "or".
2. Determine which semantic categories the following expressions relate to: a) leaves that have fallen to the ground (descriptive term, name of an object); b) leaves fell to the ground (judgment expressed in the form of a declarative sentence); c) any body immersed in a liquid is affected by a buoyant force (a judgment expressed in the form of a declarative sentence); d) will you go to the library today? (an interrogative sentence that does not contain a judgment); e) Ivan's brother (descriptive term, name of the subject).
Let us show how, using semantic categories, it is possible to identify the logical structure of thoughts. Below are four complex judgments, the structure of which must be expressed in the form of formulas using the entered logical terms.
1. If I have free time (s) and I pass the exams in pedagogy (b) and psychology (c), then I will go to rest in Crimea (d) or to the Caucasus (e).
Formula:
Here the letter a denotes the judgment: "I will have free time"; letter b- judgment: "I will pass the pedagogy exam"; letter with- judgment: "I will pass the exam in psychology"; letter d- "I will go to rest in the Crimea"; letter e- "I will go to rest in the Caucasus."
2. "If a person from childhood and youth did not let his nerves dominate over himself, then they will not get used to get irritated and will obey him." (K. D. Ushinsky).
Formula: 
Here the letter a denotes the judgment: "Since childhood, a person has given his nerves dominion over himself." And since we have a negation ("did not give"), then we write
3. "And virtue can become a vice when it is wrongly applied." (W. Shakespeare).
To reveal the structure of this judgment, one must first clearly identify the basis and the effect, and for this, this judgment should be brought to a clear logical form: “If virtue is incorrectly applied (a), then it can become a vice ( b)».
Formula:
4. "If a child has grown a rose in order to admire its beauty, if the only reward for labor was the enjoyment of beauty and the creation of this beauty for the happiness and joy of another person, he is not capable of evil, meanness, cynicism, heartlessness." (V.A. Sukhomlinsky).
Formula:
Tasks to the topic "Subject and meaning of logic"
I. Indicate the objective (denotation) and semantic (concept) meanings of the expressions: cosmonaut, metal, author of a comedy in verse "Woe from Wit", order bearer, writer, participant of the Great Patriotic War.
II. Indicate which of the given expressions are nominal functions and which are propositional; define their locality (single, or double, or triple) and get from them names or sentences that express statements (judgments) - true or false.
1 person NS redhead.
2. The difference between the numbers 15 and z.
3. Amount x 3 + y 3.
4. NS- a modern state.
5. Scientist at contemporary of the scientist z.
6. The natural number z is greater than 100.
7. River NS flows into the sea at.
8. NS, divided by 4 without remainder.
9. x 2 -y 2<7.
10. NS and at- brothers.
11. City NS located between cities at and G.
12. Major artists NS and z, who lived in the 18th century.
a) the dog barks;
b) a loud barking dog;
c) the highest mountain peak in the world;
d) a song heard in the silence of the night;
e) the song was heard in the silence of the night;
f) a performer of folk songs;
g) some figures are flat;
h) automated control system.
IV. Think up or find in the literature 2-3 complex judgments containing 5-6 simple judgments, and write down their structure using symbols.
V. Express the following complex judgments in symbolic form:
1. If you get up early at dawn and go to the garden or park, you can hear wonderful bird songs.
2. If the given quadrangle is a rhombus, then its diagonals are mutually perpendicular and divide the angles in half.
3. "Seeing injustice and being silent means participating in it yourself." (J.-J. Rousseau).
4. If you love children, are full of a thirst for knowledge, have a kind heart, dream of devoting yourself to interesting creative work, then feel free to choose the profession of a teacher.
5. "If the patient does not feel better after talking with the doctor, then this is not a doctor." (V.M.Bekhterev).
6. Good will not die, but evil will disappear.
7. A sheep raises a fleece, but a mean money saves - not about himself.
8. There will be no boredom as your hands are busy.
9. If Peter passed by the workers, he immediately undertook to help: either he would walk two rows with a scythe, or he would wind a cart, or cut down a tree, or chop wood.
10. “If a faithful horse, injuring his leg, Suddenly stumbled, and then again, Do not blame the horse, blame the road,
And do not rush to change the horse. "
(R. Gamzatov).
How do you think events would develop if the "Heilbronn Program" could be implemented?
Further destinies of Lutheranism
Luther sharply condemned the rebels and Müntzer, consolidating his alliance with the princes and the city elite. Now, after the defeat of the popular Reformation, many princes no longer viewed supporting Luther as dangerous. At the same time, they were extremely attracted by the ideas of secularization and the primacy of the sovereign over the church. Many princes went over to the side of the Reformation and took over the church domain. Even the Grand Master of the Teutonic Order dissolved the order, secularized its lands and assumed the title of Duke of Prussia. The head of the church of each principality was its sovereign.
When the Catholics were in the majority at the Reichstag in 1529 and demanded to abolish the conquests of the Reformation, Luther's supporters - Lutherans - protested. They argued that in matters of faith, the opinion of the majority cannot be imposed on the minority. From that time on, they were also called Protestants. Later this term was extended to all supporters of the Reformation in Europe.
It was not possible to reach a compromise between Protestants and Catholics, but military actions did not give an advantage to either side. The religious world imprisoned in Augsburg in 1555 recognized the equality of the two faiths. The princes received the right to determine the religion of their subjects, guided by the principle of "whose power, that is the faith." In Germany, two groupings of principalities were formed: in the south and west of the country, Catholics prevailed, in the north and east - Protestants. Relations between them remained tense.
By that time, the Reformation had long crossed the borders of Germany. Luther's supporters multiplied everywhere. At the initiative of the royal power, the Lutheran-style Reformation was carried out in England, in Denmark with Norway and Iceland under its control, in Sweden with Finland under its control. In each of these countries, the church was headed by its monarch. Thus, by the middle of the XVI century. Lutheranism prevailed in several European countries.
Let's summarize
In the first half of the XVI century. in Europe, the Reformation began - a broad movement for the complete renewal of the Catholic Church and doctrine, which covered almost all of Europe. By splitting the church, the Reformation gave rise to new directions in Christianity. The People's Reformation was defeated during the Peasant War in Germany, while Lutheranism was victorious in a number of European countries.
Theology(from the Greek theós - God and lógos - the word)- the same as theology: a systematized presentation of a doctrine, substantiating its truth and necessity for a person.
1517 The beginning of the Reformation in Germany.
1524–1525 Peasant War in Germany.
“I cannot and do not want to renounce; because acting contrary to conscience is hard, impious and dangerous. "
(From Luther's speech at the Worms Reichstag)
1. Why do you think the Reformation began in Germany?
3. Why did different directions appear in the Reformation?
4. What provisions of the programs of the Peasant War speak about the influence of the Reformation on their authors?
5. Why did the followers of the Reformation come to be called Protestants?
6. What were the results of the Reformation by the middle of the 16th century?
1. Based on the text of the paragraph, prove that the Reformation was brewing throughout Europe, and not just in Germany.
2. Determine how the following points of his theses relate to Luther's idea of justification by faith:
a) the demand for the secularization of church property;
b) condemnation of monasticism;
c) condemnation of pilgrimage;
d) reducing the number of church sacraments;
3. Determine which of the above statements belong to Luther and which to Münzer. Based on the text of the paragraph and these statements, find the differences in the views of the two reformers:
a) “When, by what commandment did God give the princes such power that we, the poor, should spend all good days in the corvee and can work in our fields only in the rain, drenched in bloody sweat? In his justice, God will not tolerate that we are constantly forced to mow their meadows, cultivate arable land ... "
