Cho mệnh đề sau: “Nếu x là một số nguyên tố lớn hơn 3 thì x2 + 20 là một hợp số (tức là số có ước khác 1 và chính nó)”.
Đáp án nào dưới đây là cách viết khác với mệnh đề đã cho?
Cho mệnh đề sau: “Nếu x là một số nguyên tố lớn hơn 3 thì x2 + 20 là một hợp số (tức là số có ước khác 1 và chính nó)”.
Đáp án nào dưới đây là cách viết khác với mệnh đề đã cho?
A. Điều kiện cần để x2 + 20 là một hợp số là x là số nguyên tố lớn hơn 3;
B. Điều kiện đủ để x2 + 20 là một hợp số là x là số nguyên tố lớn hơn 3;
C. Điều kiện cần và đủ để x2 + 20 là một hợp số là x là số nguyên tố lớn hơn 3;
D. Cả A và B đều đúng.
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Xét mệnh đê "Nếu x là một số nguyên tố lớn hơn 3 thì $x^2+$ 20 là một hợp số" ta có:
$P$ : "x là một số nguyên tố lớn hơn 3 ".
$Q$ : " $x^2+20$ là một hợp số".
Ta thấy mệnh đề trên có dạng $P \Rightarrow Q$ có thể được phát biểu dưới dạng điều kiện cần, điều kiện đủ như sau:
+ Điều kiện cần để có P là Q .
+ Điều kiện đủ để có $Q$ là $P$.
Do đó định lý đã cho được phát biểu dưới dạng điều kiện cần, điều kiện đủ lần lượt là:
+ Điều kiện cần để x là một số nguyên tố lớn hơn 3 là $x^2$ + 20 là một hợp số.
+ Điều kiện đủ để $x^2+20$ là một hợp số là $x$ là một số nguyên tố lớn hơn 3.
Đối chiếu với các đáp án trên, ta thấy mệnh đề ở đáp án B là một cách viết khác của mệnh đề đã cho.
Câu hỏi liên quan
Ion O2- không có cùng số electron với nguyên tử hoặc ion nào sau đây?
Phát biểu nào sau đây sai khi nói về quá trình tổng hợp các chất ở vi sinh vật?
Theo em, người cho vay chỉ cấp tín dụng khi có lòng tin vào việc người vay sử dụng vốn vay đúng mục đích, hiệu quả và có khả năng hoàn trả nợ đúng hạn là nói đến đặc điểm nào sau đây của tín dụng?
Trong tự nhiên nguyên tố copper (kí hiệu: Cu) có 2 đồng vị là và , trong đó đồng vị chiếm 27% về số nguyên tử. Phần trăm khối lượng của trong phân tử Cu2O là (biết rằng nguyên tử khối của O bằng 16)
MySQL có hạn chế nào sau đây?
Cho tập hợp X={1;5}, Y={1;3;5}. Tập X∩Y là
Hệ thống sông lớn duy nhất nào ở nước ta có dòng chảy đổ sang Trung Quốc?
Read the following advertisement 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 1 to 6.
MAKE MEMORIES WITH CUSTOM PHOTO BOOKS
Are you tired of digital photos sitting on your phone or computer? Turn them into beautiful custom photo books with our easy-to-use platform. Our service ___(1)___ you to upload, organize, and design your own photo book, creating a unique keepsake to treasure forever. You can ___(2)___ between different layouts, themes, and covers to make your book truly special. With our high-quality printing, your memories will ___(3)___ vibrant and long-lasting. Plus, our photo books make great gifts for family and friends. Don't ___(4)___ your memories – capture them in a book you'll love to ___(5)___ for years to come. Start designing today and ___(6)___ 20% off your first order!
Hàn Mặc Tử sinh ra trong một gia đình như thế nào?
Một sinh vật đơn bào khác một tế bào trong cơ thể sinh vật đa bào ở điểm là
Bạn T muốn mua đích đá tập võ nhưng không đủ tiền, vì vậy bạn đã tiến hành tiết kiệm tiền để thực hiện mục tiêu đó. Trong trường hợp này, bạn T nên áp dụng loại kế hoạch tài chính nào cho phù hợp?
Ở đậu Hà Lan, allele A quy định thân cao trội hoàn toàn so với allele a quy định thân thấp. Allele B quy định hoa đỏ trội hoàn toàn so với allele b quy định hoa trắng. Hai cặp gene này nằm trên 2 cặp nhiễm sắc thể tương đồng. Cho đậu thân cao, hoa đỏ dị hợp về 2 cặp gene tự thụ phấn thu được F1. Biết không xảy ra đột biến. Chọn ngẫu nhiên một cây thân cao, hoa đỏ ở thế hệ F1 cho tự thụ phấn. Xác suất thu được cây thân cao hoa đỏ ở thế hệ F2 là bao nhiêu?
Read the following passage about global warming 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 18 to 22.
ADMIRING A U.S. PRESIDENT
One of the most influential figures in American history is Franklin D. Roosevelt, who served as the 32nd President of the United States. (18) ______. He is known for his leadership during the Great Depression and World War II. His New Deal programs aimed to provide relief for the unemployed and stimulate economic recovery. Roosevelt’s ability to communicate with the American people through his fireside chats (19) ______.
His policies helped reshape the role of the federal government in the economy, leading to lasting changes that continue to impact the nation today. (20) ______. Roosevelt's vision for a more inclusive America resonated with many citizens, and his commitment to social welfare programs has left a significant legacy.
Additionally, his determination and resilience during his battle with polio (21) ______. This experience shaped his empathy for the struggles of others and influenced his approach to governance. His leadership style is often admired for its ability to unite the country in times of crisis. (22) ______. His enduring impact is evident in the policies and institutions that were established during his presidency.
Theo em phát biểu nào sau đây là sai?
Cho hai mệnh đề: \(P\): “\({2^3} \cdot {5^{2025}} \ge {7^{1000}}\)”, \(Q\): “Tổng số đo bốn góc trong một tứ giác bằng \(360^\circ \)”.
a) Mệnh đề phủ định của mệnh đề \(P\) là \(\overline P \): “\({2^3} \cdot {5^{2025}} < {7^{1000}}\)”.
b) Phát biểu mệnh đề \(P \Rightarrow Q\): “Nếu tổng số đo bốn góc trong một tứ giác bằng \(360^\circ \) thì \({2^3} \cdot {5^{2025}} \ge {7^{1000}}\)”.
c) Mệnh đề \(P \Rightarrow Q\) đúng.
d) Phát biểu mệnh đề \(P \Rightarrow Q\) bằng cách sử dụng điều kiện đủ là: “Tổng số đo bốn góc trong một tứ giác bằng \(360^\circ \) là điều kiện đủ để \({2^3} \cdot {5^{2025}} \ge {7^{1000}}\)”.
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 31 to 40.
Who are you?
On 6 June 2011, the media reported the kidnapping of a female Syrian-American blogger called Amina Arraf. Regarded as a daring political rebel, the 35-year-old had gained popularity for her blogs protesting the lack of freedom in Syria. Yet, only two days later, it was discovered that Amina had never existed. She was a fictional character created by Tom MacMaster, a forty-year-old American PhD student at the University of Edinburgh.
MacMaster's invention is an example of sock puppetry: the use of false identities to deceive others. (I). The false identity is known as a sock puppet, and its creator, a puppet master. (II). MacMaster created Amina to express his views on Middle Eastern affairs without offending other Americans. (III). Writing as Amina gave him the authority to say what he wanted. (IV).
At the turn of the millennium, Debbie Swenson created Kaycee Nicole, a fictional teenage girl suffering from terminal cancer. Her blog, Living Colours, described Kaycee’s struggle, attracting millions of readers. When Kaycee 'died' on 14 May 2001, her fans were devastated. Their distress turned to anger when they discovered that Kaycee was not real. Swenson had developed the character to gain attention and sympathy.
While Amina and Kaycee were used to meet their creators' needs, other identities have been invented for profit. American gun advocate John Lott made up a fake student, Mary Rosh, to defend his writing online and give him positive reviews. Mystery writer RJ Ellory fabricated a team of sock puppets to praise his own books and tear into those of his rivals. British historian Orlando Figes lost credibility when he had to publicly apologise for doing the same.
Yet none of these stories compare to large-scale sock puppetry today. The New York City Police Department has false identities on social media to catch criminals. The US military is believed to use sock puppets to track potential terrorists. It is clear that the internet is a minefield today and we all have to step very carefully in order not to get hurt.
Which of the following best summarizes paragraph 3?
Tác dụng của cách gieo vần “eo”:
Read the following passage about a multicultural world 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.
[I] In today’s interconnected world, multiculturalism has become increasingly prevalent as people from diverse cultural backgrounds live and work together in the same communities. [II] Multiculturalism fosters cultural diversity, promoting understanding and tolerance among individuals with different perspectives and traditions (Banks, 2015). [III] However, while multiculturalism brings many benefits, it also poses certain challenges that need to be addressed to achieve a harmonious society (Parekh, 2000). [IV]
One of the key benefits of multiculturalism is the enrichment of society through diverse perspectives. Different cultural backgrounds contribute unique ideas, art forms, and traditions, which can lead to a more vibrant and innovative community. For instance, diverse viewpoints in the workplace often drive creativity and lead to better problem-solving solutions. Additionally, exposure to various cultures can increase people's awareness and acceptance of others, thus reducing discrimination and promoting social cohesion.
However, a multicultural society is not without its challenges. Language barriers, for example, can hinder communication and understanding among individuals. Miscommunication due to language differences can lead to misunderstandings or even conflicts. Furthermore, people may feel divided by their cultural identities, which can create a sense of "us versus them." Some argue that without efforts to bridge cultural differences, multiculturalism might unintentionally lead to social fragmentation (Modood, 2007).
To foster a successful multicultural society, it is essential to promote inclusive policies and encourage intercultural dialogue. Schools and workplaces can play a significant role by celebrating diversity and teaching cultural understanding. When people actively engage with different cultures, they are more likely to find common ground and develop mutual respect, which helps create a stronger, more unified community (Berry, 2011).
Which of the following best paraphrases the underlined sentence in paragraph 4?
Read of 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.
Join Our Fitness Revolution
Are you ready to (7)________ your fitness game?
At our gym, you’ll not only find state-of-the-art equipment but also a community that motivates and supports you. Some people come for weight training, while (8)______join for cardio classes.
We offer various training (9)______, including yoga, Pilates, and strength building. (10)__________ personal training sessions, we have group classes to fit every schedule.
Our trainers are (11)__________in the fields of fitness and health, dedicated to helping you achieve your goals. Gain a new (12)________of confidence, energy, and enthusiasm from your workouts!
Don't wait to become the best version of yourself. Join us today!
Read the following passage about the impact of social media on mental health and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions
[I] In recent years, social media platforms have become a central part of daily life, offering users countless ways to connect, share, and communicate. [II] While these platforms offer many advantages, experts have noted rising concerns about their effects on mental health, particularly among young people (Smith & Anderson, 2018). [III] Studies reveal that excessive social media use can contribute to feelings of anxiety, depression, and loneliness, despite its intention to promote connection and social interaction (Twenge & Campbell, 2019). [IV]
A primary reason for these mental health concerns is the tendency for social media users to compare themselves to others. Platforms like Instagram and Facebook often highlight idealized lifestyles, leading users to feel inadequate about their own lives. Additionally, the constant notifications and messages contribute to a "fear of missing out," or FOMO, which keeps individuals in a cycle of checking their phones, often reducing the quality of sleep and overall well-being.
There is also a growing body of research suggesting a link between social media use and decreased attention spans. When users frequently switch between apps and notifications, their ability to focus for extended periods may diminish (Rosen, 2019). This shift in attention can interfere with productivity, especially in academic and professional settings, where sustained focus is essential.
Addressing these challenges requires a multi-faceted approach. Some mental health professionals suggest limiting screen time and setting boundaries, such as "device-free" hours before bedtime. Others recommend engaging in offline activities, like reading or exercising, to reduce dependence on social media and build healthier habits. According to psychologists, such strategies can bu mental resilience and allow for more meaningful, balanced relationships (Robinson & Smith, 2020).
The word "enhance" in paragraph 4 is OPPOSITE in meaning to ____.