Counterexamples

A counterexample is a single witness that DISPROVES a universal claim.

To disprove $\forall x. P(x)$, it suffices to find ONE $x$ with $\neg P(x)$.

The smallest / simplest counterexample is often the most useful for understanding
why the claim fails.

Worked counterexample. Claim: "Every prime is odd."
- Counterexample: $2$ is prime AND $2$ is even.
- Therefore the claim is false.

The lesson: a single counterexample wins over a thousand failed attempts to
prove.