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  2. In logic, a counterexample disproves a generalization1. For example, the fact that "John Smith is not a lazy student" is a counterexample to the generalization “students are lazy”1. Here are some examples of counterexamples in logic2:
    • All oranges are fruits and all oranges are citrus, so all citrus are fruits.
    • No actors are politicians, so no politicians are insensitive, since no actors are insensitive.
    • Some students are people who shower every day, because some students are people with jobs and some people with jobs shower every day.
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    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 both are counterexample to, and disproof of, the generalization “all students are lazy.”

    en.wikipedia.org/wiki/Counterexample

    Solutions to Counter-example exercises

    • 1. All oranges are fruits and all oranges are citrus, so all citrus are fruits. Form: ...
    • 2. No actors are politicians, so no politicians are insensitive, since no actors are insensitive. Form: ...
    logic.umwblogs.org/validity/validity-exercises/soluti…
     
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