3.2 Truth Tables for Negation, Conjunction, and Disjunction 119 57. Chicago is in India or Los Angeles is in the United States, or Tokyo is in Canada. True 58. Siamese is a breed of cat and Labrador Retriever is a breed of dog, or beagle is not a type of bird. True Five Most Populated Countries in 2022 In Exercises 59–62, use the table to determine the truth value of each simple statement. Then determine the truth value of the compound statement. Countries with the Highest Population in 2022 Country Population (in millions) China 1425.9 India 1417.1 United States 338.3 Indonesia 275.5 Pakistan 235.8 59. China had a greater population than India and India had a greater population than Pakistan. True 60. The United States had over twice the population of Indonesia or China had over twice the population of India. False 61. The population of India and the United States combined was greater than the population of China, and the population of Indonesia and Pakistan combined was not greater than the population of the United States. False 62. The population of the United States was not greater than the population of China, but the population of India was greater than the population of Indonesia. True Sleep Time In Exercises 63– 66, use the graph, which shows the number of hours Americans sleep, to determine the truth value of each simple statement. Then determine the truth value of the compound statement. 63. It is false that 30% of Americans get 6 hours of sleep each night and 9% get 5 hours of sleep each night. True 64. Twenty-five percent of Americans get 6 hours of sleep each night, and 30% get 7 hours of sleep each night or 9% do not get 5 hours of sleep each night. True 8 hours or more, 32% 4 or fewer, 4% 5 hours, 9% Hours of Sleep 6 hours, 25% 7 hours, 30% 39. School is not in session and the kids are home, or I am working. * 40. The dryer is loud or I am drying shoes, and I cannot fix dinner. * In Exercises 41–50, determine the truth value of the statement if a) p is true, q is false, and r is true. b) p is false, q is true, and r is true. 41. ∧ ∼ ∨ p q r ( ) a) True b) True 42. ∧ ∼ ∨ p q r ( ) a) True b) False 43. ∼ ∧ ∼ ∨ ∼ p q r ( ) a) False b) False 44. ∼ ∧ ∼ ∨ ∼ p q r ( ) a) False b) False 45. ∨ ∼ ∧ ∼ ∧ ∼ p q p r ( ) [ ( )] a) True b) False 46. ∧ ∼ ∨ p q r ( ) a) True b) True 47. ∼ ∧ ∨ r p q ( ) a) False b) True 48. ∼ ∨ ∧ q r p ( ) a) True b) False 49. ∼ ∨ ∼ ∨ ∼ ∨ p q r q ( ) ( ) a) True b) True 50. ∼ ∧ ∼ ∧ ∼ ∨ ∼ r q r p ( ) ( ) a) False b) False In Exercises 51–58, determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. (You may have to use a reference source such as the Internet.) 51. + = − 8 7 20 5and ÷ = × 63 7 3 3 True 52. < − 0 3 or ≥ 5 10 False 53. Florence is in Italy or London is in France. True m London 54. A nectarine is a fruit and a banana is a vegetable. False 55. George Washington was the first U.S. president or Abraham Lincoln was the second U.S. president, but Harry Truman was not the third U.S. president. True 56. Apple makes cars or Samsung makes blue jeans, and Nike makes sneakers. False *See Instructor Answer Appendix S4svisuals/123RF
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