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Mastering Inductive and Deductive Reasoning

Learn to use inductive reasoning to draw general conclusions from specific examples. Prove specific conclusions with deductive reasoning based on general statements. Explore examples and strengthen your argument skills.

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Mastering Inductive and Deductive Reasoning

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  1. 1.1 Inductive and Deductive Reasoning

  2. Objectives Understand and use inductive reasoning. Understand and use deductive reasoning.

  3. Inductive Reasoning • The process of arriving at a general conclusion based on observations of specific examples. • Definitions: • Conjecture/hypothesis: The conclusion formed as a result of inductive reasoning which may or may not be true. • Counterexample: A case for which the conjecture is not true which proves the conjecture is false.

  4. Strong Inductive Argument • In a random sample of 380,000 freshman at 772 four-year colleges, 25% said they frequently came to class without completing readings or assignments. We can conclude that there is a 95% probability that between 24.84% and 25.25% of all college freshmen frequently come to class unprepared. • This technique is called random sampling, discussed in Chapter 12. Each member of the group has an equal chance of being chosen. We can make predictions based on a random sample of the entire population.

  5. Weak Inductive Argument • Men have difficulty expressing their feelings. Neither my dad nor my boyfriend ever cried in front of me. • This conclusion is based on just two observations. • This sample is neither random nor large enough to represent all men.

  6. Example 2a: Using Inductive Reasoning • What number comes next? • Solution: Since the numbers are increasing relatively slowly, try addition. • The common difference between each pair of numbers is 9. • Therefore, the next number is 39 + 9 = 48.

  7. Example 3: Fibonacci Sequence • What comes next in this list of numbers? 1, 1, 2, 3, 5, 8, 13, 21, ? • Solution: This pattern is formed by adding the previous 2 numbers to get the next number: • So the next number in the sequence is: 13 + 21 = 34

  8. Deductive Reasoning • The process of proving a specific conclusion from one or more general statements. • Theorem: A conclusion proved true by deductive reasoning

  9. An Example in Everyday Life

  10. Homework Pg 9: 1 – 27 odd, 39 – 45 odd

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