Patterns, Inductive Reasoning & Conjecture

Inductive Reasoning

• Inductive reasoning is reasoning that is based on patterns you observe.

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You Try!

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Conjecture

• A conclusion you reach using inductive reasoning.

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• What conjecture can you make about the twenty-first term in R, W, B, R, W, B, . . . ?

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• What conjecture can you make about the first 30 odd numbers?

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Counterexamples

• Not all conjectures will turn out to be true, you should always test your conjecture, to prove a conjecture false you only need to find one counterexample.

• Counterexample is an example that shows a conjecture is incorrect.

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You Try!

• Write a counterexample for each conjecture.– If a flower is red it is a rose. – One and only one plane exists through any

three points– When you multiply a number by three the

product is divisible by six.