A universal affirmative claim has the form “Every A is B.” To refute it, one verified instance that is A but not B is enough.
Claim: Every student is present.
Counterexample: Ahmad is a student and is absent today.
Conclusion: “Every student is present” is false.
One confirming case does not establish a universal claim, whereas a genuine counterexample can refute it. This asymmetry is important in assessing induction.
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Induction: Complete and Incomplete Enumeration, Certainty and Probability
A universal affirmative claim has the form “Every A is B.” To refute it, one verified instance that is A but not B is enough.
Claim: Every student is present.
Counterexample: Ahmad is a student and is absent today.
Conclusion: “Every student is present” is false.
One confirming case does not establish a universal claim, whereas a genuine counterexample can refute it. This asymmetry is important in assessing induction.