Illustrated definition of Counterexample: An example that disproves a statement (shows that it is false). Example: the statement all dogs are hairy...

The existence counterexample proves the statement is false, even if it is often, mostly, or almost entirely true. Counterexamples are incredibly important for logic, which is, in turn, important …

A counterexample is an example in which the condition is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false.

Things to remember A counterexample to a mathematical statement is an example that satisfies the statement's condition (s) but does not lead to the statement's conclusion. Identifying …

In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical …

To make a counterexample in math, first, find an example that satisfies the conditions of the theorem. Then, demonstrate that the example proves the opposite of the conclusion of the …

In mathematics, a counterexample is typically used to disprove a conjecture or to show that a theorem is false in some cases. To provide an example, consider the statement “all even …

A counterexample is a specific instance that disproves a general statement or conjecture. If a proposition P says “for all objects x, property Q (x) holds,” then a counterexample is an object …

Sep 8, 2025 · Thus, that example which made the statement false is called the counterexample. Counterexamples are used in the fields of mathematics, science, and philosophy to prove any …

There exists at least one element y y of the set S S such that the property P P does not hold. It follows immediately by De Morgan's laws that if Y Y is true, then X X must be false. Such a …