150 CHAPTER 3 Logic Solution This argument contains three simple statements. Let p q r : My cell phone company is Verizon. : I can call you free of charge. : I can send you a text message. In symbolic form, the argument is written as follows. p q q r r p p → ∨ ∨ ∴ Write the argument in the form p q q r r p p [( ) ( ) ( )] . → ∧ ∨ ∧ ∨ → Now construct the truth table (Table 3.36). The answer, column 7 of the truth table, is not true in every case. Thus, the argument is a fallacy, or invalid. Now try Exercise 47 Table 3.36 p q r p q [( ) → ∧ q r ( ) ∨ ∧ r p ( )] ∨ → p T T T T T T T T T T T T F T T T T T T T T F T F F T F T T T T F F F F F F T T T F T T T TTTT F F F T F T T T F F T F F F T T T T T T F F F F F T F F F F T F 1 3 2 5 4 7 6 7 Let’s now investigate how we can arrive at a valid conclusion from a given set of premises. Determine Logical Conclusions Example 7 Determine a Logical Conclusion Determine a logical conclusion that follows from the given statements. “I will attend the concert or I will attend the volleyball game. I will not attend the concert. Therefore …” Solution If we recognize a specific form of an argument, we can use our knowledge of that form to draw a logical conclusion. Let p q : I will attend the concert. : I will attend the volleyball game. The argument is of the following form: p q p~ ? ∨ ∴ If the question mark is replaced with q, this argument is of the form disjunctive syllogism. Thus, a logical conclusion is “Therefore, I will attend the volleyball game.” 7 Now try Exercise 59 Instructor Resources for Section 3.5 in MyLab Math • Objective-Level Videos 3.5 • PowerPoint Lecture Slides 3.5 • MyLab Exercises and Assignments 3.5 PhotoProCorp/Shutterstock
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