Cho mệnh đề P(x): "∀x∈R, x2+x+1>0". Mệnh đề phủ định của mệnh đề P(x) là
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Trong trường hợp này, $P(x)$ là $x^2 + x + 1 > 0$, vậy $\overline{P(x)}$ là $x^2 + x + 1 \le 0$.
Do đó, mệnh đề phủ định của $\forall x\in \mathbb{R},\text{ }{{x}^{2}}+x+1>0$ là $\exists x\in \mathbb{R},\text{ }{{x}^{2}}+x+1\le 0$.
Câu hỏi liên quan
Read the following passage about food addiction and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Few people would disagree that one of the world's most popular dishes is pizza. Twenty-two-year-old Zack certainly wouldn't. He would eat a variety of pizza-based items, including homemade pizza, precooked microwave pizza, and even pizza leftovers from the night before. He was consuming 800kg of pizza a year. As a child, Zack had eaten a wide variety of food. But he became addicted to pizza when he started secondary school. American school meals have often been criticised for the large amount of fast food present on the menu, and pizza is the star dish. Zack even spent all his pocket money on slices of pizza.
Naturally, Zack's family worried about his high-calorie, low-vitamin diet. So did Zack. In an attempt to break his addiction, Zack agreed to appear on a TV programme called Freaky Eaters. Its aim was to encourage food addicts to beat their addictions with the help of a psychologist and nutritionist. It wasn't easy. He had to eat a fish dish, while his brother sat in front of him enjoying... a pizza! However, Zack met the challenge and has never eaten pizza again.
Seventeen-year-old Stacy Irvine's friends visit her and discover that she has been rewarded thousands of free toys from fast food restaurants as a regular customer. Stacy's mother often gave her two-year-old girl a portion of fried chicken in a McDonald's restaurant. [I] Since then, Stacy has refused to eat anything else except for pieces of fried chicken, and as a result, her diet has created serious health. She has been warned that if she doesn't change her diet, she will die. [II] Stacy once collapsed due to lack of vitamins and nutrients and needed to be hospitalised. [III] She insisted that Stacy adopt a healthier lifestyle. However, worryingly, Stacy's mother said that while Stacy was beginning to understand the seriousness of her situation, she couldn't eat anything else but chicken nuggets. [IV]
Twenty-year-old Hanna Little was keen on chips. The only thing that Hanna consumed for fifteen years was one plate of chips after another. Not surprisingly, a diet that contained few nutrients and an excess of fat and carbohydrates could only have negative consequences. And it did because not only did Hanna develop health problems, but she also had to leave her job after collapsing at work. At five, Hanna became addicted to chips and refused to eat fruits and vegetables despite her mother's efforts. Hanna says that she was terrified of tasting the flavour of different types of food and she would feel anxious just at the idea of doing it. Parties, picnics and barbecues with friends and family used to be a nightmare. Furthermore, Hanna was soon seen as 'odd' by her friends' parents.
It wasn't until the age of sixteen that Hanna realised she had Selective Eating Disorder (SED). Despite this new knowledge, no solution was found. It wasn't until she lost her job before she started eating normally. Hanna sought therapy from psychologist Felix Economakis, who used hypnosis, a treatment that none of the doctors that she had seen before had mentioned, to get her to eat fruit after one one-hour session, and since then she has been willing to eat anything.... including chips!
(Adapted from Friends Global)
Which of the following can be inferred from the passage?
Nội dung nào sau đây thể hiện đặc điểm của ngân sách nhà nước?
Trong công nghiệp chlorine-kiềm, dung dịch sodium chloride (NaCl) bão hoà có nồng độ khoảng 300 g L⁻¹ chỉ được điện phân một phần thành “nước muối nghèo” có nồng độ 220 g L⁻¹. “Nước muối nghèo” sau đó được dẫn ra khỏi bề điện phân, trong khi nước muối bão hoà mới được bơm vào. Việc làm này giúp hạn chế sự tạo thành các sản phẩm không mong muốn của quá trình điện phân. Trong khi đó, dung dịch NaOH (xút) thu được tại cathode có nồng độ khoảng 32% được chuyển sang thiết bị cô đặc để sản xuất xút có nồng độ mong muốn, ví dụ xút 45%, xút 50%. Giả sử xút không bị thất thoát trong quá trình cô đặc, thể tích dung dịch NaCl thay đổi không đáng kể trong quá trình điện phân. Để sản xuất được một thùng 20 lít xút 50% thương phẩm có khối lượng riêng là 1,52 g mL⁻¹, cần điện phân x lít dung dịch NaCl bão hoà.
Tính giá trị của x (làm tròn đến một chữ số thập phân).
Biểu diễn dữ liệu logic trong thực tế có thể được thể hiện dưới dạng nào sau đây?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Happiness is a universal goal, yet its ingredients differ across societies and cultures. For some, safety and security are paramount, as demonstrated by Singapore. Known for its strict laws and highly regulated environment, Singapore provides a clean, orderly, and safe place for its citizens. The government ensures access to basic necessities such as housing and healthcare, significantly reducing poverty and promoting equality. While personal freedoms may be limited, many Singaporeans find satisfaction in the stability and quality of life their country offers, showing that happiness can stem from collective security.
In contrast, Mexico highlights the importance of social connections in achieving happiness. Despite challenges like poverty and limited access to essential resources, Mexicans often prioritize relationships with family, friends, and neighbors. Simple acts like sharing meals or gathering in the community foster a sense of belonging and emotional well-being. Psychologists have long noted that feeling part of a larger social group can be a powerful source of happiness, even when material wealth is scarce. For them, the joy derived from relationships often outweighs material concerns.
The role of money in happiness, however, is often debated. In Mexico, many individuals live in similar financial conditions, reducing the pressure of economic competition. When neighbors lack expensive possessions, individuals are less likely to feel dissatisfied with their own circumstances. This suggests that relative wealth and equality may have a stronger influence on happiness than absolute income.
Ultimately, there is no universal recipe for happiness. Factors like security, freedom, social bonds, and financial equality all play a role, but their importance varies depending on individual and cultural values. Happiness, therefore, remains a deeply personal and multifaceted pursuit, shaped by our unique perspectives and circumstances.
According to the passage, which of the following is NOT a factor contributing to happiness in Singapore?
Ngành công nghiệp điện lực là một trong hai ngành cơ sở hạ tầng cần ưu tiên nào trong phát triển kinh tế?
Đối tượng nghiên cứu của sử học là gì?
Thang nhiệt độ chúng ta vẫn dùng hằng ngày là thang Celsius, được đặt theo tên của nhà khoa học Thụy Điển Anders Celsius, người đầu tiên xây dựng thang nhiệt độ này vào năm 1742. Trong các phát biểu dưới đây, phát biểu nào là đúng, phát biểu nào là sai khi nói về thang nhiệt độ này?
Chọn ý đúng: Bào quan nào bao phủ các tế bào nhân sơ?
Read the following leaflet and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 7 to 12.
Eat Well, Live Well: Simple Steps for Better Health
Learn how small changes in your diet can make a big difference.
Common issues we face:
We tend to ___(7)___ too much sugar and processed food today, which can lead to health problems. Another challenge is finding time to prepare meals at home, causing a reliance on fast food. Over time, this habit increases the risk of obesity and ___(8)___ diseases.
What we can do:
● ___(9)___ on sugary drinks and replace them with water or herbal tea. This helps reduce excess calories.
● Prepare meals at home ___(10)___ buying pre-made options, giving you control over ___(11)___ and portion sizes.
● When shopping, look for fresh fruits and vegetables rather than processed foods. They provide a(n) ___(12)___ of nutrients essential for good health.
Ba đỉnh cao Thơ mới của Chu Văn Sơn gồm những tác giả nào?
Cung cấp một nhiệt lượng 61600 J để nung nóng một khối kim loại nặng 1 kg từ 20 oC lên 90 oC. Nhiệt dung riêng của khối kim loại này là bao nhiêu J/kg.K?
Nội dung nào dưới đây nói về đặc điểm hoạt động của Hội đồng nhân dân?
Cho hàm số \(y=f\left( x \right)=\text{tan}2x-1\).
Khi nói về sự sinh trưởng của quần thể vi sinh vật, phát biểu nào đúng?
Trong mặt phẳng tọa độ Oxy, đường tròn \((C)\) đi qua hai điểm \(A(1;2),B(4;1)\) và có tâm thuộc đường thẳng \(d:2x-y-5=0\). Tính bán kính đường tròn \((C)\) (nhập đáp án vào ô trống).
Mark the letter A, B, C or D on your answer sheet to indicate the correct option that best fits each of the numbered blanks from 18 to 23.
AI (Artificial Intelligence) is revolutionizing the medical field by providing more accurate diagnoses and personalized treatment plans. Since its development, AI has become increasingly integrated into healthcare, (18) ___________. One of the most prominent examples is its use in medical imaging, where AI-powered systems are capable of detecting diseases, like cancer, with remarkable precision.
AI systems are particularly valued for their ability to process vast amounts of data quickly, enabling doctors to focus on patient care rather than administrative tasks. These advancements have led to (19) ___________, allowing for better overall outcomes. Not only does AI reduce the potential for human error, but it also continuously improves through learning from new medical data.
Medical AI systems have also (20) ___________. By analyzing genetic information and patient histories, AI can suggest potential treatment options that may have been overlooked by human experts. Moreover, these systems often lack the information needed to recommend the best treatment, ensuring that treatments are more effective and better suited to individual needs.
Despite the many benefits, some critics argue that there are still ethical concerns about the widespread adoption of AI in healthcare. For example, (21) ___________ could lead to overreliance on machines, reducing the need for skilled medical professionals. However, proponents believe that as AI continues to evolve, the medical field will revert to traditional methods By working alongside human experts, AI has the potential to transform healthcare, making it more efficient and accessible for all.
In summary, the rise of AI in medicine is an exciting development that shows great promise. It is essential (22) ___________. As these technologies advance, doctors may struggle to trust AI in complex cases.
Khi các nguyên tử tiến lại gần nhau để hình thành liên kết hoá học, sự tiếp xúc đầu tiên giữa hai nguyên tử sẽ xảy ra giữa
Ở sát mặt Trái Đất, vectơ cường độ điện trường hướng thẳng đứng từ trên xuống dưới và có độ lớn vào khoảng 150 V/m. Tính hiệu điện thế giữa một điểm ở độ cao 2,4 m và mặt đất.
Cuộc kháng chiến chống quân Thanh (1789) của nhân dân ta không mang đặc điểm nào sau đây?