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What is a counterexample?

Back

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

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If it is an angle, then it is acute. What is a counterexample?

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120° is a counterexample because it is an angle that is not acute.

Tags

CCSS.7.G.B.5

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True or False: A counterexample proves a conjecture to be true.

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False. A counterexample disproves a conjecture.

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True or False: To disprove a conjecture, only one counterexample is needed.

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True. One counterexample is sufficient to disprove a conjecture.

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What is the next term in the sequence: 1, 3, 7, 15, 31, ___?

Back

63 is the next term.

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the sequence: 1, 3, 7, 15, 31, 63, ___?

Back

127 is the next term.

Tags

CCSS.HSF.BF.A.2

Front

If an animal is furry, then it is a hamster. What is a counterexample?

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A cat is a counterexample because it is furry but not a hamster.

Front

Define conjecture in mathematics.

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

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What is the purpose of finding a counterexample?

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The purpose is to show that a conjecture is false.

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What does it mean if a conjecture is true?

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It means that there are no counterexamples that disprove it.