please answer questions 2,4,6,16,21,22,23,24,33,48,50, and 58

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120 CHAPTER 3 Log Exercise Set 3.1 College Students Business Majors In Exercises 25-28, use the representations shown at the bottom the previous column to express each symbolic statement in What can you conclude about the resulting verbal statement 26.-9 27.- wote 25. P 2. equivalent way In Exercises 57-56, Express each with "all," "son b. Write the negar 51. Nobody doesn't ta 52. A problem well st 53. Nothing is both sa 54. Many a person ha 55. Not every great a 56. Not every genero In Exercises 29-42, a. Express the quantified statement in an is, in a way that has exactly the same meaning b. Write the negation of the quantified statement. (The ne te should begin with "all," "some," or "no") 29. All whales are mammals. 30. All journalists are writers. 31. Some students are business majors. 32. Some movies are comedies. 33. Some thieves are not criminals. 34. Some pianists are not keyboard players. 35. No Democratic presidents have been impeached 36. No women have served as Supreme Court justices. 37. There are no seniors who did not graduate. 38. There are no applicants who were not hired. 39. Not all parrots are pets. 40. Not all dogs are playful. 41. All atheists are not churchgoers. 42. All burnt muffins are not edible. Application Exerc In Exercises 57 and 58 57. The City Council citizens that in th the city to its a did not keep its Therefore, durin a. No major to b. Atleast one C. Practice Exercises In Exercises 1-14, determine whether or not cach sentence is a statement 1. René Descartes came up with the theory of analytic geometry by watching a fly walk across a ceiling, 2. The number of US patients killed annually by medical errors is equivalent to four jumbo jets crashing each week. 3. On January 20, 2013, Mitt Romney became America's 45th president 4. On January 20, 2009, Barack Obama became America's first Hispanic president 5. Take the most interesting classes you can find. 6. Don't try to study on a Friday night in the dorms. 7. The average human brain contains 100 billion neurons. 8. There are 2.500,000 rivets in the Eiffel Tower. 9. Is the unexamined life worth living? 10. Is this the best of all possible worlds? 11. All US presidents with beards have been Republicans. 12. No U.S. president was an only child. 13. The shortest sentence in the English language is "Go!" 14. Go! In Exercises 15-20, form the negation of each statement 15. It is raining. 16. It is snowing. 17. "Facts do not cease to exist because they are ignored." -Aldous Huxley 18. "I'm not anti-social. I'm just not user friendly" T-Shirt (In this case, form the negation of both statements.) 19. It is not true that chocolate in moderation is good for the heart 20. It is not true that Albert Einstein was offered the presidency of Israel In Exercises 21-24, let p, q, r, and s represent the following statements: p: One works hard. q: One succeeds r: The temperature outside is not freezing. s: It is not true that the heater is working. Express each of the following statements symbolically 21. One does not work hard. 22. One does not succeed. 23. The temperature outside is freezing. 24. The heater is working. According to Condensed Knowledge: A Deliciously Irreverent Guide to Feeling Smart Again (Harper Collins, 2004), each statement listed below is false. p: Listening to classical music makes infants smarter. q: Subliminal advertising makes you buy things r Sigmund Freud's father was not 20 years older than his mother s Humans and bananas do nor share approximately 60% of the same DNA structure Here's another list of false statements from Condensed Knowledge p. No Africans have Jewish ancestry. q: No religious traditions recognize sexuality as central to their understanding of the sacred. r. All rap is hip-hop s: Some hip-hop is not rap. In Exercises 43-46, use the representations shown to express each symbolic statement in words Verbal statements should begin wit "all," "some," or "no. "What can you conclude about each result verbal statement? was not op At least one was open d. The airport 58. During the Wa Nixon assured public service indicated that in his years of c. 43.-P 44.-9 45.- 46.5 a. Nixon alw b. Nixon som Nixon som d. Nixon ney Our culture celebra for another person graph illustrates th important role in Practice Plus Exercises 47-50 contain diagrams that show relationships between two sets. (These diagrams are just like the Venn diagrams studied in Chapter 2. However, the circles are not enclosed in a rectangle representing a universal set.) Use each diagram to write a statement beginning with the word "all," "some," or "no" that illustrates the relationship between the sets b. Determine if the statement in part (a) is true or false. If false, write its negation. Parrots 48. Humans 60% 51% 50% 40% 47. 30% Birds 20% Mammals 10% 0 Pakistas Source: Robert Lev SOS SECTION 3.1 Statements, Negations, and Quantified Statements 121 50. 49. College Students Business Majors College Students Athletes was shown at the bottom bolie statement in word 18 verbal statement? DO 00 28. in an equivalent way, the ame meaning statement (The negation "no") In Exercises 51-56, a. Express each statement in an equivalent way that begins with "all," "some," or "no" b. Write the negation of the statement in part (a). 51. Nobody doesn't like Sara Lee. 52. A problem well stated is a problem half solved. 53. Nothing is both safe and exciting. 54. Many a person has lived to regret a misspent youth. 55. Not every great actor is a Tom Hanks, 56. Not every generous philanthropist is a Bill Gates. is. Empeached Durt justices. rate. hired. c. ndensed Knowledge elity as central to Application Exercises In Exercises 57 and 58, choose the correct statement. 57. The City Council of a large northern metropolis promised its citizens that in the event of snow, all major roads connecting the city to its airport would remain open. The City Council did not keep its promise during the first blizzard of the season. Therefore, during the first blizzard: a. No major roads connecting the city to the airport were open b. At least one major road connecting the city to the airport was not open At least one major road connecting the city to the airport was open d. The airport was forced to close. 58. During the Watergate scandal in 1974, President Richard Nixon assured the American people that "In all my years of public service, I have never obstructed justice." Later, events indicated that the president was not telling the truth. Therefore, in bis years of public service: a. Nixon always obstructed justice. b. Nixon sometimes did not obstruct justice. c. Nixon sometimes obstructed justice. d. Nixon never obstructed justice. Our culture celebrates romantic love-affection and sexual passion for another person-as the basis for marriage. However, the bar graph illustrates that in some countries, romantic love plays a less important role in marriage. Percentage of College Students willing to Marry without Romantic Love In Exercises 59-66, use the graph at the bottom of the previous column to determine whether each statement is true or false. If the statement is false, write its negation. 59. A majority of college students in Pakistan are willing to marry without romantic love. 60. Nearly half of India's college students are willing to marry without romantic love. 61. No college students in the United States are willing to marry without romantic love. 62. All college students in Pakistan are willing to marry without romantic love. 63. Not all college students in Mexico are willing to marry without romantic love. 64. Not all college students in England are willing to marry without romantic love. 65. The sentence "5% of college students in Australia are willing to marry without romantic love" is not a statement. 66. The sentence "12% of college students in the Philippines are willing to marry without romantic love" is not a statement. Writing in Mathematics 67. What is a statement? Explain why commands, questions, and opinions are not statements. 68. Explain how to form the negation of a given English statement. Give an example. 69. Describe how the negation of statement p is expressed using symbols. 70. List the words identified as quantifiers. Give an example of a statement that uses each of these quantifiers. 71. Explain how to write the negation of a quantified statement in the form "All A are B." Give an example. 72. Explain how to write the negation of a quantified statement in the form "Some A are B." Give an example. 73. If the ancient Greek god Zeus could do anything, could he create a rock so huge that he could not move it? Explain your answer. Critical Thinking Exercises Make Sense? In Exercises 74–77, determine whether each statement makes sense or does not make sense, and explain your reasoning. 74. I have no idea if a particular sentence is true or false, so I cannot determine whether or not that sentence is a statement. 75. "All beagles are dogs" is true and "no beagles are dogs" is false, so the second statement must be the negation of the first statement. 76. Little Richard's "A-wop-bop-a-lula-a-wop-bam-boom!" is an exclamation and not a statement. 77. Researchers at Cambridge University made the following comments on how we read: It deson't mtater waht oerdr the Itteres in a wrod are, so Inog as the frist and Isat Itteer are in the crorcet pclae. Tihs is bcuseae we dno't raed ervey Iteter but the wrod as a wlobe. Because of the incorrect spellings in these sentences, neither sentence is a statement. 78. Give an example of a sentence that is not a statement because it is true and false simultaneously. 79. Give an example in which the statement "Some A are not B" is true, but the statement "Some B are not A" is false. 80. "The statement She isn't dating him because he is muscular is confusing because it can mean two different things Describe the two different meanings that make this statement wwn to express each should begin with about each resulting 46. - ationships between diagrams studied rectangle used in a 60% 51% 49% eginning with the Es the relationship 50% 40% ue or false 30% 20% 18% 10% sals 10% 4% Pakistan India Thailand Mexico England US. mahir
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