gen-briefly-explain-a-counterexample-and-one-common-misconceptio-9bea

Briefly explain a counterexample and one common misconception about it.

## Counterexample A **counterexample** is a specific example that disproves a general statement or claim. If someone says "All X have property Y," finding just one X that doesn't have property Y is enough to prove the statement false. **Example:** The claim "All prime numbers are odd" is disproven by the counterexample 2, which is prime but even. ## Common Misconception **Misconception: "One confirming example proves a general statement true."** Many people mistakenly believe that if they find an example where a statement works, it proves the statement is always true. This is backwards logic—while one counterexample *disproves* a universal claim, one (or even many) confirming examples doesn't *prove* it. You would need to verify the statement for *all* possible cases, not just the ones you've checked. For instance, checking that 3, 5, and 7 are odd primes doesn't prove all primes are odd—you'd need to verify every prime number, which is impossible to do by example alone.