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- Counterexamples of numbers include123:
- A rational number that is not positive (e.g., -5)
- An even prime number (e.g., 2)
- A quadratic equation with only one root (e.g., x^2 = 0)
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Example: Tell whether the statement is True or False, then if it is false, find a counter example: If a number is a rational number, then the number is positive. Solution: This statement is false, -5 is a rational number but not positive.www.khanacademy.org/test-prep/praxis-math/praxi…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.sites.millersville.edu/bikenaga/math-proof/countere…Examples of Counterexamples in Mathematics:
- Prime numbers: The statement “all prime numbers are odd” is false because the counterexample of 2 shows that there is at least one even prime number. Therefore, 2 is a counterexample to the statement.
clubztutoring.com/ed-resources/math/counterexam… - People also ask
Counterexamples | Lesson (article) | Lessons | Khan Academy
- 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 counterexamples is a way to show that a mathematical statement is false.
- When identifying a counterexample, See more
- What is a counterexample?
- A mathematical statement is a sentence that is either true or false.
- [Examples]
- A mathematical statement has two parts: a condition and a concl… See more
• Identifying a counterexample to a mathematical statement See more
- When identifying a counterexample, follow these steps:
- 1.Identify the condition and conclusion of the statement.
- 2.Eliminate choices that don't satisfy the statement's condition. See more
- A mathematical statement is a sentence that is either true or false.
- [Examples]
- A mathematical statement has two parts: a condition and a conclusion.
- [Example] See more
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