For each statement in the **Proof Examples **collection you must first decide whether the statement is true or not. If you believe the statement to be untrue then find a single example when the statement fails (**Disproof by Counterexample**). Alternatively, if you think the statement is true then decide whether to prove it by **Proof by Deduction** or **Proof by Exhaustion**. If you are unsure, then you might like to try testing the statement with various examples first. Be sure to try the statement with negative numbers as well as positive ones. However, note that showing that the statement is true for a few examples does not prove it – see common mistakes below.