2 CHAPTER 1 Critical Thinking Skills The science of biometrics involves the measurement and analysis of unique physical characteristics. Biometrics are usually used as a means of verifying personal identity. Fingerprints, iris patterns in eyes, facial recognition, DNA, and voice patterns can all be used for personal identification. Some smartphones can be unlocked by pressing a button that recognizes a unique fingerprint or by using facial recognition. Crime scene investigation often involves fingerprint and DNA evidence. Voice recognition software uses voice patterns of callers to help prevent fraud and to improve customer service. Inductive and Deductive Reasoning SECTION 1.1 LEARNING GOALS Upon completion of this section, you will be able to: 7 Understand and use inductive reasoning to solve problems. 7 Understand and use deductive reasoning to solve problems. Why This Is Important Using biometrics for personal identification involves reasoning to a general conclusion through observation of specific cases. In this section, we will discuss how inductive and deductive reasoning are essential critical thinking skills used in biometrics and in many other applications. Inductive Reasoning Before looking at some examples of inductive reasoning and problem solving, let us first review a few facts about certain numbers. The natural numbers or counting numbers are the numbers 1, 2, 3, 4, 5, 6, 7, 8, .… The three dots, called an ellipsis, mean that 8 is not the last number but that the numbers continue in the same manner. A word that we sometimes use when discussing the counting numbers is “divisible.” If a b ÷ has a remainder of zero, then a is divisible by b. The counting numbers that are divisible by 2 are 2, 4, 6, 8, .… These numbers are called the even counting numbers. The counting numbers that are not divisible by 2 are 1, 3, 5, 7, 9, .… These numbers are the odd counting numbers. When we refer to odd numbers or even numbers, we mean odd or even counting numbers. Recognizing patterns is sometimes helpful in solving problems, as Examples 1 and 2 illustrate. Example 1 The Product of Two Even Numbers If two even numbers are multiplied together, will the product be an even number or an odd number? Solution To answer this question, we will examine the products of several pairs of even numbers to see if there is a pattern. 2 2 4 4 4 16 6 6 36 2 4 8 4 6 24 6 8 48 2 6 12 4 8 32 6 10 60 × = × = × = × = × = × = × = × = × = We see that all the products are even numbers. Thus, we might predict from these examples that the product of any two even numbers is always an even number. 7 Now try Exercise 25 Fernando Astasio Avila/123RF
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