2.1 Inductive reasoning, conjectures, and counterexamples

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The type of reasoning where a person makes conclusions based on observations and patterns is called...

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Inductive reasoning

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What are the next two numbers in this pattern: 12, 17, 22, 27, ___, ___?

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32, 37

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Make a conjecture about the next item in the sequence: –4, –1, 2, 5, 8, ...

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Add the previous number by 3

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Make a conjecture about the next item in the sequence: –2, 4, –8, 16, –32, ...

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Multiply the previous number by -2

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What is a conjecture?

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A statement believed to be true based on observations.

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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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Provide an example of a counterexample.

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If a conjecture states that all swans are white, a black swan serves as a counterexample.

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What is the first step in making a conjecture?

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Observe patterns or trends in data.

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How can you test a conjecture?

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By finding a counterexample or verifying it with additional observations.

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What is the role of patterns in inductive reasoning?

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Patterns help in forming conjectures based on observed data.