In logic, what is a counterexample?

In logic, what is a counterexample?

• A. A specific case that disproves a general statement
• B. A hypothesis proved true
• C. A universal claim that applies to all cases
• D. A generalization without exception

Answer: (A)

A counterexample is a specific case that disproves a general statement. In logic, many claims are universal—stating something about all cases. If you can find even one instance where the statement fails, that instance serves as a counterexample and shows the general claim isn’t true in all situations. For example, if someone says “all swans are white,” finding a single black swan breaks that universal claim. That single exception is what a counterexample is. The other descriptions don’t fit because they describe what would be true if the claim were correct (a hypothesis proved true), or they describe universal or general claims themselves rather than the act of refuting them.

A counterexample is a specific case that disproves a general statement. In logic, many claims are universal—stating something about all cases. If you can find even one instance where the statement fails, that instance serves as a counterexample and shows the general claim isn’t true in all situations. For example, if someone says “all swans are white,” finding a single black swan breaks that universal claim. That single exception is what a counterexample is.

The other descriptions don’t fit because they describe what would be true if the claim were correct (a hypothesis proved true), or they describe universal or general claims themselves rather than the act of refuting them.