An example that proves a conjecture false is called a(n) ___.
An example that proves a conjecture false is called a counterexample
An example that proves a conjecture false is called a counterexample. In mathematics, a conjecture is a statement that is believed to be true but has not been proven yet. When a counterexample is found, it means that the conjecture is not always true and there exists at least one case that contradicts it.
To illustrate this, let’s consider the following example:
Conjecture: “All prime numbers are odd.”
We believe this conjecture to be true because we know that prime numbers are only divisible by 1 and themselves, and most commonly encountered prime numbers like 2, 3, 5, 7, etc., are indeed odd. However, to disprove this conjecture, we need to find a prime number that is not odd:
Counterexample: The number 2 is a prime number but it is not odd.
By providing the counterexample of 2, we have proven that the conjecture “All prime numbers are odd” is false because not all prime numbers are odd.
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