# Maths - Proof by Contradiction

## See Also

## Flashcards

How can you prove a statement is FALSE by contradiction?

Find a counterexample.

How can you prove a statement is TRUE by contradiction?

- Negate the statement and assume it’s false.
- Prove this leads to a contradiction.

What would be the negated statement for “if $n^2$ is even, $n$ must be even”?

“there exists an odd number $n$ such that $n^2$ is even”

What would be the negated statement for “there are infinitely prime numbers”?

“there is a finite number of prime numbers”