# Disproof by Counterexample

**Disproof by counterexample** is the technique in mathematics where a statement is shown to be wrong by finding a single example for when it is not satisfied. Not surprisingly, disproof is the opposite of proof so instead of showing that something is true, we must show that it is false. Any statement that makes inferences about a set of numbers can be disproved by finding a single example for which it does not work.

## Examples

## Videos

This video shows the solutions that a student should give when tackling a basic disproof by counterexample question.

This video explores a proof exam question where the first part is a standard Proof by Deduction question and the second part requires the student to decide which proof to use – it turns out the statement isn’t true and a simple counterexample will suffice to disprove the statement.

## Extra Resources

Take the mathematical proof test – a selection of exam style questions on Proof by Deduction, Proof by Exhaustion and Disproof by Counterexample.