CHAPTER 3 Review Exercises 169 36. Lynn Swann played for the Steelers or Jack Tatum played for the Raiders. If Lynn Swann did not play for the Steelers, then Jack Tatum played for the Raiders. 37. It is not true that Altec Lansing only produces speakers or Harman Kardon only produces stereo receivers. Altec Lansing does not produce only speakers and Harman Kardon does not produce only stereo receivers. 38. We did not go to the beach and we did not find sharks’ teeth. It is false that we did go to the beach or we did find sharks’ teeth. 39. If the temperature is not above ° 32 , then we will go ice fishing at O’Leary’s Lake. The temperature is above ° 32 or we will go ice fishing at O’Leary’s Lake. In Exercises 40– 44, write the (a) converse, (b) inverse, and (c) contrapositive for the given statement. 40. If Mikel plays football, then he is a linebacker. * 41. If we take the table to Antiques Roadshow, then we will learn the table’s value. * 42. If you do not advertise, then you do not sell more doughnuts. * 43. If you do not study for the math test, then you fail the course. * 44. If you get straight A’s on your report card, then I will let you attend the prom. * In Exercises 45– 48, determine which, if any, of the three statements are equivalent. 45. a) If Caleb is a scientist, then Kennedy is a teacher. b) Caleb is not a scientist or Kennedy is a teacher. c) It is false that Caleb is a scientist and Kennedy is not a teacher. a), b), and c) are equivalent. 46. a) The screwdriver is on the workbench if and only if the screwdriver is not on the counter. b) If the screwdriver is not on the counter, then the screwdriver is not on the workbench. c) It is false that the screwdriver is on the counter and the screwdriver is not on the workbench. None are equivalent. 47. a) If + = 2 3 6, then + = 3 1 5. b) + = 2 3 6 if and only if + ≠ 3 1 5. c) If + ≠ 3 1 5, then + ≠ 2 3 6. a) and c) are equivalent. 48. a) If the sale is on Tuesday and I have money, then I will go to the sale. b) If I go to the sale, then the sale is on Tuesday and I have money. c) I go to the sale, or the sale is on Tuesday and I have money. None are equivalent. 3.5 In Exercises 49–52, determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table. 49. p q p q ~ ~ → ∴ Invalid 50. p q q r p r ∧ → ∴ → Valid 51. If Jose is the manager, then Kevin is the coach. If Kevin is the coach, then Tim is the umpire. If Jose is the manager, then Tim is the umpire. ∴ Valid 52. If the truck is a diesel, then the truck is too cold to start. The truck is too cold to start or the car has a flat tire. Therefore, the truck is not a diesel. Invalid 3.6 In Exercises 53–56, use an Euler diagram to determine whether the argument is valid or invalid. 53. All marigolds are annuals. Some tulips are annuals. Some tulips are marigolds. ∴ Invalid 54. All hackysack players are students. Joel is a hackysack player. Joel is a student. ∴ Valid 55. No Beatles are Rolling Stones. Some Rolling Stones are Small Faces. No Beatles are Small Faces. ∴ Invalid 56. All bears are furry. Teddy is furry. Teddy is a bear. ∴ Invalid 3.7 57. a) Write the corresponding symbolic statement of the circuit shown. p q r p ( ) ~ [ ] ∧ ∧ ∨ q r p p b) Construct a truth table to determine when the lightbulb will be on. The lightbulb will be on only when p q, , and r are all closed. *See Instructor Answer Appendix
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