106 CHAPTER 3 Logic In Exercises 39– 48, write the compound statement in words. Let p q : Joe has an iPad. : Brie has a MacBook. 39. q∼ * 40. p∼ * 41. p q ∧ * 42. ∨ q p * 43. p q ∼ → * 44. p q ∼ ↔∼ * 45. p q ∼ ∨ ∼ * 46. q p ( ) ∼ ∨ * 47. p q ( ) ∼ ∧ * 48. p q ∼ ∧ ∼ * In Exercises 49–56, write the statements in symbolic form. Let ° p q r : The temperature is 90 . : The air conditioner is working. : The apartment is vacant. 49. The temperature is ° 90 and the air conditioner is not working, and the apartment is vacant. p q r ( ) ∧ ∼ ∧ 50. The temperature is not ° 90 and the air conditioner is working, but the apartment is vacant. p q r ( ) ∼ ∧ ∧ 51. The temperature is ° 90 and the air conditioner is working, or the apartment is vacant. ∧ ∨ p q r ( ) 52. If the temperature is ° 90 , then the air conditioner is working or the apartment is not vacant. p q r ( ) → ∨ ∼ 53. If the apartment is vacant and the air conditioner is working, then the temperature is ° 90 . ∧ → r q p ( ) 54. The temperature is not ° 90 if and only if the air conditioner is not working, or the apartment is not vacant. p q r ( ) ∼ ↔∼ ∨ ∼ 55. The apartment is vacant if and only if the air conditioner is working, and the temperature is ° 90 . ↔ ∧ r q p ( ) 56. If the air conditioner is working, then the temperature is ° 90 if and only if the apartment is vacant. → ↔ q p r ( ) In Exercises 57– 66, write each symbolic statement in words. Let ° p q r : The water is 70 . : The sun is shining. : We go swimming. 57. p q r ( ) ∨ ∧ ∼ * 58. ∧ ∨ p q r ( ) * 59. p q r ( ) ∼ ∧ ∨ * 60. → ∨ q p r ( ) * 61. r q p ( ) ∼ → ∧ * 62. ∧ → q r p ( ) * 63. → ∧ q r p ( ) * 64. p q r ( ) ∼ → ∨ * 65. ↔ ∧ q p r ( ) * 66. → ↔ q p r ( ) * Dinner Menu In Exercises 67–70, use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or pasta, and carrots or peas. Which of the following selections are permissible? If a selection is not permissible, explain why. See the discussion of the exclusive or on page 98. "All dinners are served with a choice of: soup or salad, potatoes or pasta, and carrots or peas" Welcome to ANTONIO’S RESTAURANTE 67. Soup, salad, and peas Not permissible; you cannot have both soup and salad. The or used on menus is the exclusive or. 68. Salad, pasta, and carrots Permissible 69. Soup, potatoes, pasta, and peas * 70. Soup, pasta, and potatoes * In Exercises 71–79, (a) select letters to represent the simple statements and write each statement symbolically by using parentheses if necessary and (b) indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. 71. Johnny started the bonfire and Jaci did not forget the marshmallows. a) b m ∧ ∼ b) Conjunction 72. If the meeting is in Las Vegas, then we can see a show or we can go to the casino. a) m s c ( ) → ∨ b) Conditional m Las Vegas Dragon Images/ Shutterstock RebeccaAng/RooM the Agency/Alamy Stock Photo *See Instructor Answer Appendix
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