130 CHAPTER 3 Logic 56. Quentin Tarantino is a movie director, or if Michelle Yeoh is a school teacher then Michael B. Jordan is a circus clown. True 57. Independence Day is in July and Labor Day is in September, if and only if Thanksgiving is in April. False 58. Hyundai makes automobiles or Reebok makes motorcycles, if and only if Lexus makes potato chips. False In Exercises 59– 62, use the information provided about the moons for the planets Jupiter and Saturn to determine the truth values of the simple statements. Then determine the truth value of the compound statement. Metis Leda Pan Tethys Telesto Calypso Dione Helene Rhea Titan Hyperion Iapetus Phoebe Atlas Prometheus Pandora Epimetheus Janus Mimas Enceladus Himalia Lysithea Elara Ananke Carme Pasiphae Sinope Adrastea Amalthea Thebe Io Europa Ganymede Callisto Moons of Jupiter Moons of Saturn Diameter of moons: 6–49 miles 50–499 miles Source: Time.com Water ice Both Atmosphere May have: 500–999 miles 1000–3161 miles 59. Jupiter’s Moons Io has a diameter of 1000–3161 miles or Thebe may have water, and Io may have atmosphere. True 60. Moons of Saturn Titan may have water and Titan may have atmosphere, if and only if Janus may have water. False 61. Moon Comparisons Phoebe has a larger diameter than Rhea if and only if Callisto may have water ice, and Calypso has a diameter of 6–49 miles. False 62. Moon Comparisons If Jupiter has 16 moons or Saturn does not have 18 moons, then Saturn has 7 moons that may have water ice. True College Credits In Exercises 63 and 64, use the graph to determine the truth value of each simple statement. Then determine the truth value of the compound statement. The following graph shows the number of credits in various categories needed by Arturo to earn his Associate in Arts degree from Van Pelt University. Communications, 9 Electives, 21 Cultural issues, 6 Humanities, 6 Mathematics, 6 Natural sciences, 6 Social sciences, 6 Credits Needed for an A.A. Degree 63. The number of communications credits needed is more than the number of mathematics credits needed and the number of cultural issues credits needed is equal to the number of humanities credits needed, if and only if the number of social sciences credits needed is more than the number of natural sciences credits needed. False 64. If the number of elective credits needed is 21 or the number of communications credits needed is 15, then the number of humanities credits needed is equal to the number of mathematics credits needed. True In Exercises 65– 68, suppose both of the following statements are true. p: Jasmine attended the art show. q: Jasmine received the outstanding artist award. Determine the truth values of each compound statement. 65. If Jasmine received the outstanding artist award, then Jasmine attended the art show. True 66. If Jasmine did not receive the outstanding artist award, then Jasmine attended the art show. True 67. Jasmine did not receive the outstanding artist award if and only if Jasmine attended the art show. False 68. If Jasmine did not receive the outstanding artist award, then Jasmine did not attend the art show. True Concept/Writing Exercises 69. A New Computer Your parents make the following statement to your sister, “If you get straight A’s this semester, then we will buy you a new computer.” At the end of the semester your parents buy your sister a new computer. Can you conclude that your sister got straight A’s? Explain. * 70. Job Interview Consider the statement “If your interview goes well, then you will be offered the job.” If you are interviewed and then offered the job, can you conclude that your interview went well? Explain. * *See Instructor Answer Appendix
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