Counterexample – Explanation and Examples. A counterexample is a specific example for which a statement is untrue. The existence counterexample proves the statement is false, even if it is often, mostly, or almost entirely true.

Use the following information for Examples 1 and 2: A car salesman sold 5 used cars to five different couples. He noticed that each couple was under 30 years old. The following day, he sold a new, luxury car to a couple in their 60’s. The salesman determined that only younger couples by used cars.

Counter Examples. Arron Kau contributed. The Multiple Scenarios skill is very similar to Case checking and Counter Examples, though it may not be immediately obvious how to proceed. You will have to carefully determine the scenarios, and consider each of them before making the final judgement.

On the other hand, consider n = 5. While n = 5 is not divisible by 4, n2 = 25 is also not divisible by 4. For n = 5, the “if” and “then” parts of the statement are both false. Therefore, n = 5 is not a counterexample to the statement. Example. Consider real-valued functions defined on the interval 0 ≤ x ≤ 1. Give a counterexample ...

Counter-Examples. Tatiana Georgieva, Calvin Lin, and Jimin Khim contributed. Some questions ask you to find a counter-example to a given statement. This means that you must find an example which renders the conclusion of the statement false.