Ask questions and answers about logical reasoning ~ ~! !

In a murder case, there are two suspects A and B, and four other witnesses are being questioned.

The first witness said, "I only know that A is innocent."

The second witness said, "I only know that B is innocent."

The third witness said, "At least one of the first two testimonies is true."

The fourth witness said, "I'm sure the testimony of the third witness is false."

Through investigation and study, it has been confirmed that the fourth witness is telling the truth, so who is the murderer?

A: It has been proved that the fourth witness is telling the truth, so the testimony of the third witness is false, thus: "At least one of the first two testimonies is true." Is false, so: "At least one of the first two testimonies is true." The proposition of "no": "The first two testimonies are false" is true.

All I know is that A is innocent. wrong

All I know is that B is innocent. wrong

Both A and B are murderers.

Two: known conditions: there are five rooms and five different colors; There is a person of different nationalities living in each room; Everyone is drinking a specific brand of drinks; Smoking a specific brand of cigarettes; Keep a specific pet; No two people smoke the same brand of cigarettes, drink the same brand of drinks or keep the same pet. At the same time also know:

1, the British live in a red house.

2. Swedes have dogs.

3. Danes drink tea.

The green house is next to the white house on the left.

5. The owner of the green house drinks coffee.

6. People who smoke PALL MALL brand cigarettes keep birds.

7. People in the yellow house smoke Dunhill cigarettes.

8. People who live in the middle house drink milk.

9. The Norwegians live in the first house (the far left).

10. People who smoke mixed cigarettes are adjacent to people who own cats.

1 1. Horse breeders are adjacent to smokers in Dunhill Road.

12. People who smoke BLUEMASTER drink beer.

13, Germans smoke prince cigarettes.

14, Norwegians are adjacent to people who live in blue houses.

15, smoking blended cigarettes is adjacent to people who drink mineral water.

Question: Who is raising fish?

Answer:

Norway, Denmark, Britain, Germany, Sweden, yellow, blue, red, green, white mineral water, tea, milk, coffee and beer. Dunhill mixed Prince PALL MALL, EMASTER, cat, horse, bird, fish and dog, so he was German.

Seven problems of classical logical reasoning

One,

Mr q plays games with Mr s and Mr p. Mr. Q wrote a number on two pieces of paper. These two numbers are both

Is a positive integer, and the difference is 1. He put a piece of paper on Mr. S's forehead and another on Mr. P's forehead. So,

Two people can only see the numbers on each other's foreheads.

Mr. Q kept asking: Can any of you guess the number on your head?

Mr. S said, "I can't guess."

Mr. P said, "I can't guess either."

Mr. S added, "I still can't guess."

Mr. P added, "I can't guess either."

Mr. s still can't guess; Mr. P can't guess either.

Mr. S and Mr. P guessed three times, but they didn't get it right.

However, by the fourth time, Mr. S shouted, "I know!" " "

Mr. P also shouted, "I know!" "

Q: What are the numbers on the heads of Mr. S and Mr. P?

Second,

There is a cell with three prisoners. Because the glass is thick, three people can only see each other, but can't hear.

The voice of the other party. "

One day, the king thought of a way to put a hat on each of them and let them know the hat.

The children are either white or black, so they don't know what color their hats are. in?that?case

Next, the king announced the following two items:

1. Whoever can see the other two prisoners wearing white hats will be released;

Whoever knows that he is wearing a black hat will be released.

In fact, the king wears black hats for them. They can't see themselves because they are tied up. So the three of them

People stare at each other and don't talk. Soon, however, A, a conscientious man, decided by reasoning that he was wearing a black hat. you want

, how did he infer?

Third,

There is a very old village. There are two kinds of people in this village, red eyes and blue eyes. Both kinds of people are nothing.

Yao is different. No one knew what color his eyes were before the baby was born. There is a wide village in the middle.

Tian is a place where villagers gather. Now there are only three people in this village.

Live in three places. In this village, there is a rule that if a person can know the color of his eyes, at night,

If he kills himself, he will go to heaven. These three people can't tell each other the color of their eyes in words, nor can they use them.

How to tell each other what color their eyes are, and you can't use a mirror.

Water and other reflective substances can see the color of their eyes. Of course, they are not blind. They can see each other.

Eyes, but just can't tell him! They can only think with their minds, so they come to the square early every morning.

In fact, sitting face to face, thinking about the color of your eyes, day by day passed.

There was no progress until one day, a foreigner came and said a word in the square, which changed him.

Our destiny, he said, at least one of you has red eyes. Say that finish and left. Listen, these three people.

After that, they sat face to face in the evening and went back to sleep. The next day, they came again.

I came to the square and sat for another day. That night, the two committed suicide successfully! On the third day, when the last person

When I came to the square, I saw that the two men didn't come, and I knew that they had succeeded in committing suicide, so he also went back, and so did that night.

Successful suicide!

According to the above, please tell the colors of three people's eyes and tell the reasoning process!

Fourth,

Two houses are next to each other. Three switches in one house control three light areas in the other house.

You can only enter these two houses once. How do you know which switch controls which light?

Five,

There are 9 points, arranged as follows:

. . .

How to connect these nine points with four straight lines (these four straight lines are required to be continuous)

Seven,

There is a river with hunters and wolves, a man with two children and a woman with two children.

If the hunter leaves, the wolf will eat everyone. If the man leaves, the woman strangles her two children.

If a woman leaves, there is a boat in the river that can only carry two people (additional conditions: only hunters, male or female)

Can row a boat). Q: How did these eight people cross the river (all on one side of the river, the wolf counts as one)?

The answer to the question 1: Three times is wrong. Four times is right ... it should be 3 and 4.

Question 2: Suppose three prisoners are named A.B.C.A They use empathy. A first stands in the perspective of B; So A stands in C's point of view: Therefore, both B.C. saw two black hats. Then A can prove that he is wearing a black hat. So his reasoning satisfied the king's second condition.

Answer three questions

On their first day home, they didn't commit suicide. It is impossible to have only 1 red eye, only 2 or 3.

Going home the next day, two suicides showed two red eyes because they saw 1 blue eyes 1 red eyes.

On the third day, 1 came. Naturally, I know I have blue eyes.

If they all come, they all have red eyes.

Answers to four questions

Superior room 1 turn on the light 1, burn in March, then turn on the light 1 to room 2.

Go into room 2 and turn on the light in the same way.

Finally, look out of the window at 1.

Five answers

Seeing the sloppy king I saw when I was a child.

Answer six questions

1 Hunt werewolves in the past

The hunter is back.

The hunter and her two children went there (in batches).

The Borzoi is back.

Men and women in the past

Six women are back.

The Borzoi passed by.

Eight people came back.

The past nine men and women

10 The woman is back.

1 1 women 1 children pass by

The hunter wolf is back.

13 hunter children expired

14 The hunter is back.

15 hunter wolf past events

call it a day

1. Lao Zhong started smoking again after giving up smoking for a month. Strangely, this is supported by Mrs. Zhong. Mrs. Zhong said, "There are two directors in our director's office. They are about the same age and look similar in physical condition, except for one who is a heavy smoker and one who never smokes. However, the recent physical examination found that this person who never smokes has lung cancer, and it is not necessarily good not to smoke. "

If the following items are true, which one can refute Mrs. Zhong's inference? ()

A. The causes of difficult diseases such as cancer are the research topics of many medical researchers, and there is no conclusion yet.

B. The report of the World Conference on Women shows that women often work in the kitchen, and the proportion of lung cancer is relatively high because of oil smoke.

Most of the causes of cancer are related to patients' personality and emotions. Many non-smokers are prone to cancer because of long-term depression.

D According to statistics, 75% of lung cancer patients have a long-term smoking history, while only 30% of adults have a long-term smoking history.

It is acknowledged that the ancestors of North Americans came from Asia. How did Asians get to North America? Scientists have always assumed that Asians crossed the land connecting North America and Asia before 14000 years, and then sank to the bottom of the sea. During the difficult migration, they hunted animals on land along the way. Recent discoveries have led to a new hypothesis that Asians enter North America by boat along the southern coast of the land, feeding on fish and marine life along the way.

Which of the following, if true, gives people the most reason to believe the latter of the two hypotheses? ()

A. When North America and Asia were still connected, Asians mainly hunted animals on land for a living.

B The land connecting North America and Asia is extremely cold, and the species and quantity of plants are extremely scarce, which makes it impossible to maintain the survival of animals.

C In Europe, the marine culture that relies on marine life as a food source for human beings originated 10000 years ago.

The cultures of Asia and North America, which existed 8000 years ago, show great similarities.

In recent years, the increase in the number of surgeons has exceeded the increase in the number of surgical operations, and many previously necessary surgical operations can now be replaced by medical care. In this way, in recent years, the number of operations performed by each surgeon has decreased by an average of one quarter every year. If this trend is not reversed, the overall quality and level of surgery will inevitably decline.

Which of the following assumptions is the above argument based on? ()

A. It is impossible for a surgeon to maintain his surgical level unless the number of operations he performs every year is not lower than a minimum standard.

B. The operation level of new surgeons is generally lower than that of existing surgeons.

C in recent years, the number of surgical operations has been decreasing year by year.

Some experienced surgeons have done more operations every year in recent years than before.

Three athletes from Liaoning, Shandong and Hebei participated in the women's 5000m competition in the National Games. Before the game, four sports fans got together to predict the result of the game. A said: "Liaoning team has a set of training, and the top three this time are none other than them." B said, "This year is different from last year. The Liaoning team won a gold, silver and bronze medal at most. " C said: "According to my estimation, Shandong team or Hebei team will win the card." Ding said: "If the first place is not Liaoning, it should be Shandong." After the game, I found that only one of the four people was right.

Which of the following is the most likely result of the game? ()

A. First place Liaoning team, second place Liaoning team and third place Liaoning team.

B: Liaoning team is the first, Hebei team is the second and Shandong team is the third.

C The first team was Shandong, the second team was Liaoning and the third team was Hebei.

D. First place Hebei team, second place Liaoning team and third place Liaoning team.

Japanese talk show performer Kim Lou Yu has obtained many patents. There is a kind of

The idea of installing a small drawer instead of an ashtray on a lighter won a grand prize in a creative competition and was highly respected. After the competition, a lighter manufacturer in Tokyo further developed this idea into a product and put it on the market. As a result, sales are not ideal.

Which of the following, if true, can best explain the above contradiction? ()

A. An ashtray manufacturer introduced a new type of ashtray at the same time, which can attract many consumers.

B: The price of this new lighter is 20 yen more expensive than that of ordinary lighters, which some consumers think is not worth it.

C. Many smokers think that playing with cigarette ash anywhere is unsightly and unhygienic, and it is easy to burn clothes.

D. Many manufacturers chose this idea to develop and produce and put it on the market almost at the same time after participating in the creative competition.

6. The rapid development of China is tied to enterprises; The rapid development of enterprises depends on entrepreneurs. Therefore,

China's rapid economic development urgently needs a large number of outstanding entrepreneurs.

Which of the following logical reasoning methods is the same as the above reasoning method? ()

A. There are blue balls in the red box and green balls in the blue box. Therefore, it is impossible to put the green ball in the red box.

B New technology increases the technological content and value of products, and products with low technological content have low value.

C. Productivity determines production relations, and production relations determine superstructure. Superstructure reacts on productivity.

D. excellent academic performance comes from diligence, and diligence needs the support of will. Therefore, to achieve good results, we must have a tough will.

7. In product inspection, false inspection includes two situations: first, unqualified products are qualified; The second is to classify qualified products as unqualified. There are two kinds of product inspection systems, A and B, which are based on different principles, but the similarities are as follows: First, all unqualified products can be detected; Second. The false positive rate is only 3%; Third, there is no product that will be wrongly detected by two systems. Now these two systems are merged into one system, so that the system can determine nonconforming products, including and only including nonconforming products determined when the two systems work separately. It can be concluded that the false detection rate of this product detection system is 0.

Which of the following can best evaluate the above reasoning? ()

A. The above reasoning is inevitable, that is, if the premise is true, the conclusion must be true.

B. The above reasoning is strong, but not inevitable, that is, if the premise is true, it provides strong evidence for the conclusion, but additional information may still weaken the argument.

C. the above reasoning is very fragile. Although the premise is related to the conclusion, it only provides insufficient basis for the conclusion at most.

D. This reasoning does not hold water, because it takes the basis of the necessary condition of an event as the basis of the sufficient condition.

1. answer a.

Analysis of Mrs. Zhong's reasoning process is that some people smoke without cancer, but non-smokers do, so smoking has nothing to do with cancer. To refute this inference, we only need to prove that most smokers have a high probability of getting cancer, or that non-smokers will get cancer for other reasons. B, C and D are all reasons for refutation, and only A has nothing to do with reasoning.

2. answer b

To deny the former and affirm the latter, we must find out the conditions that can weaken the former and strengthen the latter's argumentation ability at the same time, and item B meets this requirement. Because of the cold land climate and lack of food resources at the junction, it is less likely to enter North America from land. In contrast, marine food is rich, which can maintain the energy demand of Asians during migration.

Step 3 answer a

The proposition revealed by stem analysis is that the overall quality and level of surgery will also decline, because the number of operations performed by doctors has decreased. Obviously, there is a lack of a condition, that is, to establish the relationship between the level of surgery and the number of operations, which can be expressed as that if the number of operations per year does not reach a certain standard, his technical level will decline, which is option A.

4. answer d

If the predictions of A and C are contradictory, then one of them must be right. In this way, both Ding and B are wrong, that is to say, the top three teams in Liaoning have not only won one, but Liaoning and Shandong have not won the first place. Therefore, the order of the top three teams is: Hebei, Liaoning and Liaoning. The answer is D.

5. answer d

The new ashtray in analysis option A is different from the lighter in the title, so A's explanation is not sufficient. The "partial" consumers in item B are universal; Item c explains the opposite. So the answer is d.

6.answer d

Analyze this problem and examine the transitivity of necessary conditions.