# Counterexample

How to solve counterexample problems: meaning, examples, and their solutions.

## What is it?

A counterexample is an example

that makes a statement to be false.

Only one counterexample is needed

to prove the statement to be false.

## Example 1

If *x* = 2,

then *p* is true (2 is a prime number)

and *q* is false (2 is not an odd number).

So *p* → *q* is false.

Conditional statement: truth value

So the counterexample is *x* = 2.

## Example 2

If three points are on a same line,

then those three points

cannot determine a triangle.

So it makes the given statement to be false.

So the counterexample is

'three points on a same line'.

To make this statement to be true,

it should be like this:

three non-linear points determine a triangle.