What is counterexample? Explain the use of counterexample with the help of an example.
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a
proposed general rule. For example, consider the proposition "all students are lazy". Because this statement makes
the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will
prove it false. Thus, any hard-working student is a counterexample to "all students are lazy". More precisely, a
counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).
In mathematics, this term is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full
hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can
show that the conclusion does not hold.[citation needed]A counterexample may be local or global in an argument.
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Suppose that a mathematician is studying geometry and shapes, and she wishes
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