IGNOU MCS 13 2012 - What is counterexample? Explain the use of counterexample with the hel

Question

What is counterexample? Explain the use of counterexample with the help of an example.

02 Nov 2017

Answer :

Word Count : 441

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

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