counterexample
An example used to show that a given statement is not always true.
A counterexample is an instance or situation that contradicts or disproves a statement or proposition. In other words, it is an example that can be used to show that a statement or claim is false, invalid or incorrect. Counterexamples are commonly used in mathematics and logic to demonstrate that a general statement or theorem is not universally true.
For example, let’s say someone makes the claim that all birds can fly. A counterexample to this claim would be the flightless birds, such as ostriches, emus, and penguins, because they are birds but they cannot fly.
Another example is the statement all prime numbers are odd. A counterexample to this statement would be the number 2, which is a prime number but is even.
Counterexamples can be useful in disproving conjectures, verifying the accuracy of statements, and developing new theories or hypotheses. They help to clarify and refine our understanding of concepts and provide a way to test the validity of mathematical and logical arguments.
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Compound Statements In Logic And Programming: Examples In MathThe Importance Of Negation In Communication And Critical Thinking: A Guide.
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