A-10 ANSWERS 12. a) p q p q p q ( ) ( ) ( ) ⎣⎡ ∧∼ ∨∼∧ ⎤⎦∨ ∧ b) The lightbulb will be on in all cases except when p and q are both open. 13. p q r 14. r p q 15. r p q 16. p q r 17. p q r s 18. q s p r 19. p q r p q 20. p q p r q 27. It is a series circuit; therefore, both switches must be closed for current to flow and the lightbulb to go on. When the p switch is closed, the p switch is open and no current will flow through the circuit. When the p switch is closed, the p switch is open and no current will flow through the circuit. 28. It is a parallel circuit; therefore, only one of the switches must be closed for current to flow and the lightbulb to go on. Since the p switch and the p switch cannot both be open at the same time, current will always flow through one or the other branch of the parallel circuit to make the lightbulb go on. 29. p q p q REVIEW EXERCISES, PAGE 168 5. The coffee is hot or the coffee is strong. 6. The coffee is not hot and the coffee is strong. 7. If the coffee is hot, then the coffee is strong and the coffee is not Maxwell House. 8. The coffee is Maxwell House if and only if the coffee is not strong. 9. The coffee is not Maxwell House, if and only if the coffee is strong and the coffee is not hot. 10. The coffee is Maxwell House or the coffee is not hot, and the coffee is not strong. 17. F F T F 18. T F F F 19. T T T T T F F T 20. T F T T F F F F 21. F T F F T T T T 22. F T T T T T T T 40. a) If Mikel is a linebacker, then he plays football. b) If Mikel does not play football, then he is not a linebacker. c) If Mikel is not a linebacker, then he does not play football. 41. a) If we will learn the table’s value, then we take the table to Antiques Roadshow. b) If we do not take the table to Antiques Roadshow, then we will not learn the table’s value. c) If we will not learn the table’s value, then we do not take the table to Antiques Roadshow. 42. a) If you do not sell more doughnuts, then you do not advertise. b) If you advertise, then you sell more doughnuts. c) If you sell more doughnuts, then you advertise. 43. a) If you fail the course, then you do not study for the math test. b) If you study for the math test, then you do not fail the course. c) If you do not fail the course, then you study for the math test. 44. a) If I let you attend the prom, then you will get straight A’s on your report card. b) If you do not get straight A’s on your report card, then I will not let you attend the prom. c) If I will not let you attend the prom, then you did not get straight A’s on your report card. 58. q p p q
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