Problem Solving.pptx - Problem Solving Inductive and Deductive Reasoning Inductive Reasoning The process of reaching a general conclusion by examining

Problem Solving.pptx - Problem Solving Inductive and...

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Problem Solving Inductive and Deductive Reasoning
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Inductive Reasoning The process of reaching a general conclusion by examining specific examples. Conjecture - The conclusion formed by using inductive reasoning.
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Example: Use inductive reasoning to predict the next number in each of the following lists. a. 3, 6, 9, 12, 15, ? b. 1, 3, 6, 10, 15, ? Answer: a. 18 b. 21
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Exercise: Use inductive reasoning to predict the next number in each of the following lists. a. 5, 10, 15, 20, 25, ? b. 2, 5, 10, 17, 26, ? Use Inductive Reasoning to Make a Conjecture: Consider the following procedure: Pick a number. Multiply the number by 8, add 6 to the product, divide the sum by 2, and subtract 3. Complete the above procedure for several different numbers. Use inductive reasoning to make a conjecture about the relationship between the size of the resulting number and the size of the original number.
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Counterexamples A statement is a true statement provided that it is true in all cases. If you can find one case for which a statement is not true, called a counterexample , then the statement is a false
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Verify that each of the following statements is a false statement by finding a counterexample. For all numbers x : a. I x I > 0 b. x^2 > x c. X^ 2 ^ 1/2 Solution
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