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- To find a counterexample, you need to12345:
- 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 statement's conclusion isn't true.
- Construct an argument with the same form that is obviously invalid.
- Consult a list of known counter-examples.
- Try to construct the specific counter-example you have in mind.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.When identifying a counterexample, follow these steps: 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 statement's conclusion isn't true.www.khanacademy.org/test-prep/praxis-math/praxi…To give a counterexample, we need to find the square of an integer such that it is divisible by 4 Let's try with 6! 62 6 2 is divisible by 4 but 6 is not divisible by 4 Thus n = 6 is a counterexample to Jim's statement. ∴ ∴ n = 6 is the counterexamplewww.cuemath.com/data/counterexample/The "counterexample method" is a powerful way of exposing what is wrong with an argument that is invalid. If we want to proceed methodically, there are two steps: 1) Isolate the argument form; 2) Construct an argument with the same form that is obviously invalid. This is the counterexample.www.thoughtco.com/prove-argument-invalid-by-co…To give a counterexample, I have to find an integer n such n2is divisible by 4, but n is not divisible by 4 — the “if” part must be true, but the “then” part must be false. Consider n = 6. Then n2= 36 is divisible by 4, but n = 6 is not divisible by 4. Thus, n = 6 is a counterexample to the statement. On the other hand, consider n = 5.sites.millersville.edu/bikenaga/math-proof/countere…9 Answers
- 1) Consult a list of known counter-examples. This is a really good strategy in subjects like analysis and topology. I don't know how well it works in algebra, but I expect there are several known pathological counter-examples. ...
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