Proof by counterexample

#counterexample#disproof#universal statement

Statement

Disprove: "every prime is odd".

Hint

Find a prime that is not odd.

Show solutionHide solution

Counterexample. $2$ is prime, but $2$ is even, hence not odd.

Conclusion. The statement "every prime is odd" is false; $2$ is a counterexample.