Lesson 2.1 Inductive Reasoning and Conjectures

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What is Inductive Reasoning?

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Inductive Reasoning is the process of testing and observing patterns to make conjectures.

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What is a conjecture?

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A conjecture is a statement that is believed to be true based on observations but has not yet been proven.

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How can you prove a conjecture is false?

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You can prove a conjecture is false by providing a counterexample.

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What is a counterexample?

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A counterexample is an example that disproves a conjecture or statement.

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If x^2 = 4, what is a counterexample to the conjecture that x = 2?

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x = -2 is a counterexample to the conjecture.

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For the statement 'For all numbers a, 2a + 7 ≤ 17', what is a counterexample?

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a = 6 is a counterexample to the statement.

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What is the rule for the pattern 65, 62, 59, 56, 53, 50?

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The rule for the pattern is to subtract 3.

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What is the difference between inductive reasoning and deductive reasoning?

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Inductive reasoning involves making generalizations based on specific observations, while deductive reasoning involves drawing specific conclusions from general principles.

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What is the importance of counterexamples in mathematics?

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Counterexamples are important because they help to test the validity of conjectures and statements.

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Can a conjecture be proven true?

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A conjecture can be proven true through a formal proof or by showing that it holds for all cases.