144 CHAPTER 3 Logic Recreational Mathematics 76. Kakuro Refer to the Recreational Math box on page 133. Complete the following Kakuro puzzle. * 18 23 15 20 14 30 12 16 9 11 6 11 19 11 12 11 22 17 19 16 22 16 15 17 6 34 21 22 4 11 15 16 9 16 12 14 17 13 16 12 Research Activities 77. Fuzzy Logic Review the Mathematics Today box regarding fuzzy logic on page 139 and Exercise 75. Do additional research and write a report on how fuzzy logic is used in many devices we encounter in our everyday lives. 78. Lewis Carroll Read one of Lewis Carroll’s books and write a report on how he used logic in the book. Give at least five specific examples. 79. Augustus De Morgan Do research and write a report on the life and achievements of Augustus De Morgan. Indicate in your report his contributions to sets and logic. *See Instructor Answer Appendix SECTION 3.5 LEARNING GOALS Upon completion of this section, you will be able to: 7 Determine the validity of a symbolic argument by using truth tables or by using standard arguments. 7 Determine a logical conclusion from a given set of premises. Consider the following statements. If we go to the Bahamas, then we will go snorkeling. We go to the Bahamas. What logical conclusion can you draw from these two statements? Do you agree that you can logically conclude that We will go snorkeling? In this section, we will use our knowledge of logic to study the structure of such statements to draw logical conclusions. Symbolic Arguments Why This Is Important We often learn information that allows us to draw conclusions from this information. In this section we will study how we can use logic to draw such conclusions using what are called standard arguments. We will also learn how to use truth tables to determine the accuracy of conclusions drawn from a set of given logical statements. The information presented in this section can help us make wise decisions in our everyday lives. Determine the Validity of Arguments Previously in this chapter, we used symbolic logic to determine the truth value of a compound statement. We now extend those basic ideas to determine whether we can draw logical conclusions from a set of given statements. Consider once again the two statements. If we go to the Bahamas, then we go snorkeling. We go to the Bahamas. Viktor Gladkov/123RF
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