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.

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

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 …

Identify the condition and conclusion of the statement. Eliminate choices that don't satisfy the statement's condition. For the remaining choices, counterexamples are those where the …

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

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 …

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 …

To give a counterexample, I have to find an integer n such n2 is divisible by 4, but n is not divisible by 4 — the “if” part must be true, but the “then” part must be false.

Sep 8, 2025 · Counterexamples can demonstrate any statement as false, even if they appear to be true in some cases. For example, the statement “all prime numbers are odd numbers”.

In short, counterexamples refute arguments while examples support them. No amount of examples will ever prove a claim, only lend support, but it only takes a single counterexample …