3.5 Symbolic Arguments 153 52. If Xiomara runs a dance school, then Jane becomes an author. Jane becomes an author. Therefore, Xiomara runs a dance school. * 53. If you did not submit your application, then you will not be accepted to school. You did not submit your application. Therefore, you will not be accepted to school. * 54. If Bonnie passes the bar exam, then she will practice law. Bonnie will not practice law. Therefore, Bonnie did not pass the bar exam. * 55. The baby is crying but the baby is not hungry. If the baby is hungry then the baby is crying. Therefore, the baby is hungry. * 56. If the car is new, then the car has air conditioning. The car is not new and the car has air conditioning. Therefore, the car is not new. * 57. If you liked The Bachelor, then you liked The Bachelorette. If you liked The Bachelorette, then you did not like The Amazing Race. Therefore, if you liked The Bachelor, then you liked The Amazing Race. * 58. The engineering courses are difficult and the chemistry labs are long. If the chemistry labs are long, then the art tests are easy. Therefore, the engineering courses are difficult and the art tests are not easy. * In Exercises 59– 64, using the standard forms of arguments and other information you have learned, supply what you believe is a logical conclusion to the argument. Verify that the argument is valid for the conclusion you supplied. 59. If next week is spring break, then we go on vacation. Next week is spring break. Therefore, . . . Therefore, we go on vacation. 60. If the temperature hits 100 ,° then we will go swimming. We did not go swimming. Therefore, . . . Therefore, the temperature did not hit 100°. 61. I have strep throat or I have Covid. I do not have Covid. Therefore, . . . Therefore, I have strep throat. 62. If I can get Nick to his piano lesson by 3:30 p.m., then I can do my shopping. If I can do my shopping, then we do not need to order pizza again. Therefore, . . . Therefore, if I can get Nick to his piano lesson by 3:30 p.m., then we do not need to order pizza again. 63. If you close the deal, then you will get a commission. You did not get a commission. Therefore, . . . Therefore, you did not close the deal. 64. If Katherine is at her ballet lesson, then Allyson will take a nap. Katherine is at her ballet lesson. Therefore, . . . Therefore, Allyson will take a nap. Concept/Writing Exercises 65. Is it possible for an argument to be valid if its conclusion is false? Explain your answer. * 66. Is it possible for an argument to be invalid if its conclusion is true? Explain your answer. * 67. Is it possible for an argument to be invalid if the premises are all true? Explain your answer. * 68. Is it possible for an argument to be valid if the premises are all false? Explain your answer. * Challenge Problems/Group Activities 69. Determine whether the argument is valid or invalid. If Lynn wins the contest or strikes oil, then she will be rich. If Lynn is rich, then she will stop working. If Lynn does not stop working, then she did not win the contest. ∴ Valid 70. Is it possible for an argument to be invalid if the conjunction of the premises is false in every case of the truth table? Explain your answer. * Recreational Mathematics 71. René Descartes was a seventeenth-century French mathematician and philosopher. One of his most memorable statements is, “I think, therefore, I am.” This statement is the basis for the following joke. Descartes walks into an inn. The innkeeper asks Descartes if he would like something to drink. Descartes replies, “I think not,” and promptly vanishes into thin air! This joke can be summarized in the following argument: If I think, then I am. I think not. Therefore, I am not. a) Represent this argument symbolically. p q p q ~ ~ → ∴ b) Is it a valid argument? No c) Explain your answer using either a standard form of argument or using a truth table. This argument is the fallacy of the inverse. Research Activities 72. Show how logic is used in advertising. Discuss several advertisements and show how logic is used to persuade the reader. 73. Find examples of valid (or invalid) arguments in printed matter such as newspaper or magazine articles. Explain why the arguments are valid (or invalid). *See Instructor Answer Appendix Lakov Filimonov/ Shutterstock
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