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- In logic, a counterexample disproves a generalization1. For example, the fact that "John Smith is not a lazy student" is a counterexample to the generalization “students are lazy”1. Here are some examples of counterexamples in logic2:
- All oranges are fruits and all oranges are citrus, so all citrus are fruits.
- No actors are politicians, so no politicians are insensitive, since no actors are insensitive.
- Some students are people who shower every day, because some students are people with jobs and some people with jobs shower every day.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is a counterexample to the generalization “students are lazy”, and both are counterexample to, and disproof of, the generalization “all students are lazy.”
en.wikipedia.org/wiki/CounterexampleSolutions to Counter-example exercises
- 1. All oranges are fruits and all oranges are citrus, so all citrus are fruits. Form: ...
- 2. No actors are politicians, so no politicians are insensitive, since no actors are insensitive. Form: ...
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Counterexample – Explanation and Examples | The Story of …
A counterexample is a specific instance for which a given statement is false. In formal logic, a statement is “false” if it is not true in every single circumstance. Even if it is usually true or sometimes true, it is false. For this reason, finding even one case where the statement is false makes it false. Sometimes, it is … See more
Writing a counterexample requires finding a specific case when a statement is wrong and showing how the case disproves the statement. When showing that a … See more
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WEBA counter-example to an argument is a situation which shows that the argument can have true premises and a false conclusion.
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WEBA counterexample to a general proposition is one that states that the proposition is false. In particular, this chapter answers three questions: Do humans recognizes the force of …
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WEB8.4.4 Proof by Counterexample. 🔗. Suppose that we are considering a universal claim. So we might have something like one of these expressions: 🔗. [1] ∀ x (P (x)) 🔗. [2] ∀ x (∃ y (P …
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WEBA counterexample to an argument is a substitution instance of its form where the premises are all true and the conclusion is false.
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WEBExample \(\PageIndex{1}\) In Exercise 6.12.8, you are asked to prove the following statement by proving the contrapositive. If \(2^n - 1\) prime, then \(n\) is prime.
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WEBSep 12, 2018 · Counterexamples (Intro to Logic) In this video, I cover a relatively simple method for testing whether an argument is invalid known as 'counterexamples'. Still …
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WEBThere are two counterexamples to the claim that this expression is a tautology. One of them is p = True, r = True and s = False. 🔗. Exercises. 🔗. 1. Consider the claim: ¬ ( a ∧ ( b …
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WEBQuantum mechanics provides sufficient evidence for abandoning classical logic – that is, it provides a counterexample to classical logic.
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WEBDec 7, 2018 · Abstract. In “Is Logic Empirical” (Putnam 1968), Putnam formulates an empirical argument against classical logic—in particular, an apparent counterexample to …
logic - Proof by contradiction using counterexample
WEBApr 6, 2016 · Having a counterexample to A A means that we have a particular x0 x 0 such that p(x0) p (x 0) is true but q(x0) q (x 0) is false. Similarly, having a counterexample to B …
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WEBMar 9, 2016 · To give a counterexample you must interpret the argument formally, forgetting about lions & animals. The logical form is: All L's are A's, and all L's are M's; therefore …
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WEBCounterexample in propositional logic - Mathematics Stack Exchange. Ask Question. Asked 11 years, 5 months ago. Modified 11 years, 4 months ago. Viewed 1k times. 4. There is …
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