In logic (especially in its applications to mathematics and philosophy), a counterexample is an exception to a proposed general rule or law, and often appears as an example which disproves a universal statement . For example, the statement " all students are lazy " is a universal statement which makes the claim that a certain property (laziness) holds for all students . Thus, any student who is not lazy(e.g., hard-working) would constitute a counterexample to that statement. A counterexample hence is a specific instance ofthe falsity of a universal quantification (a "for all" statement ).
A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy . For example, the fact that " John Smith is not a lazy student " is a counterexample to the generalization “students are lazy”, and a both a counterexample to, and disproof of, the statement “all students are lazy.”
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In logic (especially in its applications to mathematics and philosophy), a counterexample is an
A counterexample is any
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proposed general rule or law, and often appears as an example which disproves a universal statement
generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy
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statement
fact that
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all students are lazy
John Smith is not a lazy student
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universal statement which makes the claim that a certain property (laziness) holds for all students . Thus, any student who is not lazy(e.g., hard-working) would constitute a counterexample to that statement. A counterexample hence is a specific instance ofthe falsity of a universal quantification (a "for all" statement ).
counterexample to the generalization “students are lazy”, and a both a counterexample to, and disproof of, the statement “all students are lazy.”