120 CHAPTER 3 Logic 75. To qualify for a loan of $40,000, an applicant must have a gross income of $28,000 if single, $46,000 combined income if married, and assets of at least $6,000. * Bridgett is married to Brandon. Bridgett earns $42,000 and Brandon does not have an income. Bridgett and Brandon have assets of $42,000. Jasper is not married, works in sales, and earns $31,000. He has assets of $9000. Lanny and her spouse have total assets of $43,000. One earns $35,000, and the other earns $23,500. 76. To qualify for a loan of $45,000, an applicant must have a gross income of $30,000 if single, $50,000 combined income if married, and assets of at least $10,000. * Steve, married with two children, earns $37,000. His spouse, Riley, earns $15,000 at a part-time job. Steve and Riley have assets of $25,000. Toni, single, has assets of $19,000. They work in a store and earn $25,000. Sarah earns $24,000 and Dana, her spouse, earns $28,000. Their assets total $8000. 77. Airline Special Fares An airline advertisement states, “To get the special fare you must purchase your tickets between January 1 and February 15 and fly round trip between March 1 and April 1. You must depart on a Monday, Tuesday, or Wednesday, and return on a Tuesday, Wednesday, or Thursday, and stay over at least one Saturday.” a) Determine which of the following individuals will qualify for the special fare. Xavier qualifies; the other four do not. b) If the person does not qualify for the special fare, explain why. * Xavier plans to purchase his ticket on January 15, depart on Monday, March 3, and return on Tuesday, March 18. Gina plans to purchase her ticket on February 1, depart on Wednesday, March 12, and return on Thursday, April 3. Kara plans to purchase her ticket on February 14, depart on Tuesday, March 4, and return on Monday, March 19. Christos plans to purchase his ticket on January 4, depart on Monday, March 10, and return on Thursday, March 13. Chang plans to purchase his ticket on January 1, depart on Monday, March 3, and return on Monday, March 10. Problem Solving/Group Activities In Exercises 78 and 79, construct a truth table for the symbolic statement. 78. p q q r [( ( )) ( )] ∼ ∼ ∨ ∨ ∧ * 79. q r p q p r [( ) ( )] ( ) ∧ ∼ ∧ ∼ ∨ ∼ ∨ ∨ ∼ * 65. Thirteen percent of Americans get 5 or fewer hours of sleep each night or 32% get 6 or more hours of sleep each night, and 30% get 8 or more hours of sleep each night. False 66. Over one-half of Americans get 7 or fewer hours of sleep each night, and over one-quarter get 6 or fewer hours of sleep each night. True In Exercises 67–70, let p q : Tanisha owns a convertible. : Joan owns a Volvo. Translate each statement into symbols. Then construct a truth table for each compound statement and indicate under what conditions the compound statement is true. 67. Tanisha owns a convertible and Joan does not own a Volvo. * 68. Tanisha does not own a convertible, but Joan owns a Volvo. * 69. Tanisha owns a convertible or Joan does not own a Volvo. * 70. Tanisha does not own a convertible or Joan does not own a Volvo. * In Exercises 71–74, let p q r : The house is owned by an engineer. : The heat is solar generated. : The car is run by electric power. Translate each statement into symbols. Then construct a truth table for each compound statement and indicate under what conditions the compound statement is true. 71. The car is run by electric power or the heat is solar generated, but the house is owned by an engineer. * 72. The house is owned by an engineer and the heat is solar generated, or the car is run by electric power. * 73. The heat is solar generated, or the house is owned by an engineer and the car is not run by electric power. * 74. The house is not owned by an engineer, and the car is not run by electric power and the heat is solar generated. * Obtaining a Loan In Exercises 75 and 76, read the requirements and each applicant’s qualifications for obtaining a loan. a) Identify which of the applicants would qualify for the loan. b) For the applicants who do not qualify for the loan, explain why. *See Instructor Answer Appendix Samuel Borges Photography/ Shutterstock
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