Mathematics

Mathematics

Problem

Which of the following best defines a counterexample in mathematics? a) A logical sequence that proves a conjecture false.\text{A logical sequence that proves a conjecture false.} b) A specific case that demonstrates a conjecture is false.\text{A specific case that demonstrates a conjecture is false.} c) A specific case that supports a conjecture.\text{A specific case that supports a conjecture.} d) A statement accepted without proof as true.\text{A statement accepted without proof as true.}
Intuitive explanation

A counterexample is a specific instance that disproves a general claim or statement. Rather than proving something is always true, you find just one case where it fails—and that single case is enough to show the claim is false. This is a powerful tool because disproving only requires one exception, whereas proving requires showing something works everywhere.

Intuitive explanation

A counterexample is a specific instance that disproves a general claim or statement. Rather than proving something is always true, you find just one case where it fails—and that single case is enough to show the claim is false. This is a powerful tool because disproving only requires one exception, whereas proving requires showing something works everywhere.

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