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Module 3 PROBLEM SOLVING AND REASONING Gauge Your Learning! A. Use inductive reasoning to find a pattern and predict the number or figure in the list. Then make a reasonable conjecture of the following: 1) 1, 2, 4, 7, 11, 16, 22, 29? 2) 9, 12, 11, 14, 13, 16, 15, 18? 3) -2,3, -4,5,-6,7? 4) 2,5, 10, 17, 25? 5) B. Find a counterexample to show that each statement is false. 6) The sum of any three odd numbers is even. 7) When an even number is added to the product of two odd numbers, the result will be even. 8) When an odd number is squared and divided by 2, the result will be a whole number. C. Use inductive reasoning to make a conjecture about a rule that relates the number you selected to the final answer. Prove your conjecture by using deductive reasoning. 9) Pick a number: Double it: Subtract 20 from the answer: Divided by 2: Subtract the original number: Result: 10) Pick a number: Multiply it by 9: Add 21: Divided by 3: Subtract three times the original number: Result: D. Determine whether the following statements are inductive or deductive reasoning. Write our answer after each statement. 11) Every time you eat peanuts, you start to cough. You are allergic to peanuts. 12) 1 All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown. 13) All brown dogs in the park today are small dogs. Therefore, all small dogs must be brown