Proof by Counter-Example
Find an example that will disprove the statement.
Example
Disprove the following conjecture by providing a counter example.
If n3 – n is divisible by 4, then n must be divisible by 4.
Let n = 3
∴ n3 – n = 24
24 ÷ 4 = 6
∴ n3 – n is divisible by 4
3 is not divisible by 4
∴ n is not divisible by 4
This counter example disproves the conjecture.