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Published byNoah Summers Modified over 8 years ago
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2.1 Using Inductive Reasoning to Make Conjectures
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Find the pattern If everyone at a party of people shakes everyone else’s hand one time, how many handshakes will there be? January, March, May ____________ 7,14,21,28,_________ 1,2,4,__________ ____________ people1234567….20 Hand- shakes
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Inductive Reasoning When several examples form a pattern and you assume or draw the conclusion that the pattern will continue (like on the previous slide) you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true.
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Conjecture A statement you believe to be true based on inductive reasoning. Examples: The product of an even number and an odd number is ________. The product of an even number and an odd number is ________. The sum of two odd numbers is ________. The sum of two odd numbers is ________.
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How do you show that a conjecture is always true? PROVE IT!!!
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How do you show that a conjecture is false? Find a counterexample.
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Counterexamples can be….. A drawing A statement, or A number.
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True or False? If x = 3, then x² = 9. If x² = 9, then x = 3. For every integer, n³ is positive. If the grass is wet, then it rained. If B is the midpoint of AC, then AB = BC. If AB = BC, then B is the midpoint of AC. For any real number x, x² > x. The winner of the door decoration contest will get a pizza party! ~ ~ _
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Inductive Reasoning Look for a pattern Make a conjecture Is it true? If yes, PROVE IT! If no, provide a Counterexample.
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