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You pull one out, put it back, and repeat 8 times, and each time you get a blue marble. What do you think will happen on the 9th time? You and six other people, all from New England, are in an elevator. True or False: At least two of you are from the same state. How do you know?Vt0DOt0DO  >%RInduction and DeductionWednesday 21 May 2008+The PlanM: Transformations T: Conditionals W: Inductive and Deductive Reasoning R: Practice / Assessment F: Half-Day Next Week: Course Review Following Week: Project Steamertrunk Then: Exams and GatewaysZ   !  $$((%,,00P"U  RainUIt has rained for each of the last 7 Wednesdays. What do you conclude about tomorrow?&1%1% Inductive Reasoning(Inductive reasoning is what you re doing when you look at many specific situations, and generalize to make up a rule. The last six times it has been hot and humid all day, there has been a thunderstorm in the afternoon. From this, I reason that heat and humidity are a cause of thunderstorms, and that they make thunderstorms more likely.FwX   %How to Apply InductionDLook at the data. Find a pattern. Extend the pattern. Make a ruleEZED-You Try: Applying Induction 'The Problem with InductionMaybe you just got lucky. Maybe you just got unlucky. Maybe something strange happened. The worst part: you ll never know!(~Z.NSeven People in an ElevatorYou and six other people, all from New England, are in an elevator. True or False: At least two of you are from the same state. Again, how do you know?&DVDV Deductive ReasoningYou were able to come to conclusions about these situations without asking any questions. You reasoned from the facts, and applied rules of logic. This is called deductive reasoning., Deductive Reasoning.Sort of the opposite: you apply general rules to specific situations. Mr. Quinn is 30. It s a general rule that everyone is younger than his father, so I know that Mr. Quinn s father can t be 15. Deductive reasoning is, in my opinion, cooler. You re sort of making something out of nothing. Plus, used properly, it s totally bulletproof.GPP/P_P    /_ A Classic ExamplezAll people die eventually. Mr. Quinn is a person. Therefore& The Problem with Deduction8It s not always that simple. A man sitting on top of a house, all of whose windows face north, looks out a window and sees a bear. What color is the bear?Z How to apply deduction./Carefully. Explicity. In writing. In steps.           How to apply deduction.9Make a statement. Say why that statement is true. Repeat.:n:.You Try: Deductionn(1. Jonathan gave 1 more point to the ride he tried first, than the person who tried The Wave of Insanity first, was this Tabitha? 2. The Terror Hawk Ride, which turned out to be a bit of a disappointment, was awarded 2 less points than the ride tried first by Stewart, which was not The Whopper or The Windmill Triple Looper. 3. The Coaster of Doom was tried first by a girl and scored 1 more point than the ride tried first by Ellie. 4. Bethany was absolutely thrilled with her first ride, not The Whopper, and gave it the highest number of points.)Z)? SummaryDeduction is the act of taking facts and applying rules to them to make new facts. Induction is its opposite  taking a bunch of facts and using them to make new rules up. The process: Make a statement Explain why it s true. 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