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- A counterexample is a situation which shows that a proposed general rule or law is not always true12. A counterexample can be used to disprove a universal statement or an argument by showing that it can have true premises and a false conclusion12. A counterexample is a way of demonstrating the invalidity of a deductive argument2.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 (especially in its applications to mathematics and philosophy ), a counterexample is an exception to a proposed general rule or law, and often appears as an example which disproves a universal statement.
en.wikipedia.org/wiki/CounterexampleDefinition: A counter-example to an argument is a situation which shows that the argument can have true premises and a false conclusion. If the argument being evaluated is deductive, then we can show it to be invalid and, therefore, bad if we can describe a counter-example.
www.futurelearn.com/info/courses/logical-and-critic… WEBMay 15, 2024 · The meaning of COUNTEREXAMPLE is an example that refutes or disproves a proposition or theory.
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WEBCounterexample definition: an example that refutes an assertion or claim.. See examples of COUNTEREXAMPLE used in a sentence.
A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are lazy."
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WEBA 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 …
WEBCheck pronunciation: counterexample. Definition of counterexample noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
WEBWhat is a counterexample? A mathematical statement is a sentence that is either true or false. Examples. 2. 3 5. A mathematical statement has two parts: a condition and a conclusion. Example. If an odd number and an even number are added, the sum is odd. …
WEBCounterexample. An example that disproves a statement (shows that it is false). Example: the statement "all dogs are hairy" can be proved false by finding just one hairless dog (the counterexample) like below.
WEBcounterexample. Other forms: counterexamples. Definitions of counterexample. noun. refutation by example. see more.
WEB4 days ago · an example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary. Copyright © HarperCollins Publishers. Word Frequency. counterexample in American English. …
WEBnoun. An example that refutes or disproves a hypothesis, proposition, or theorem. American Heritage. An example used to support an argument or claim that is in opposition to another argument or claim. Webster's New World. (logic) An exception to a proposed …
Counterexample - Cuemath
WEBCounterexample Definition. A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. Counterexample Math. Instead of showing …
COUNTEREXAMPLE Definition & Usage Examples | Dictionary.com
WEBCounterexample definition: . See examples of COUNTEREXAMPLE used in a sentence.
Counterexample in Mathematics | Definition, Proofs & Examples
WEBNov 21, 2023 · A counter example is an example that refutes or disproves a proposition or theory. A counterexample can be something very simple in real life. There are many counterexamples to...
Counterexample -- from Wolfram MathWorld
WEBMay 24, 2024 · A counterexample is a form of counter proof. Given a hypothesis stating that F (x) is true for all x in S, show that there exists a b in S such that F (b) is false, contradicting the hypothesis.
2.6: Conjectures and Counterexamples - K12 LibreTexts
WEBNov 28, 2020 · Definition; conjecture: A conjecture is an educated guess that is based on examples in a pattern. counterexample: A counterexample is an example that disproves a conjecture. fraction: A fraction is a part of a whole. A fraction is written mathematically …
counterexample - Wiktionary, the free dictionary
WEBJan 29, 2024 · ( logic) An example that counters a general rule; an exception to a general rule; a specific instance of the falsity of (and falsifiability of) any proposed universal applicability of a rule or statement. Derived terms [ edit] pseudo …
Counter-Examples | Brilliant Math & Science Wiki
WEBCounter-Examples | Brilliant Math & Science Wiki. Tatiana Georgieva , Calvin Lin , and Jimin Khim contributed. Some questions ask you to find a counter-example to a given statement. This means that you must find an example which renders the conclusion of …
COUNTEREXAMPLE definition in American English | Collins …
WEB3 days ago · noun. an example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary. Copyright © HarperCollins Publishers. Examples of 'counterexample' in a sentence. counterexample.
Counterexample: Definitions and Examples - Club Z! Tutoring
WEBA counterexample is a specific example that disproves a general statement. It is a powerful tool in mathematics and other fields where statements are made about general cases. A counterexample can be used to demonstrate that a statement is false, even if it …
Counter-example - definition of Counter-example by The Free …
WEBan example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, …
6.7: Proof by counterexample - Mathematics LibreTexts
WEBDefinition: Counterexample. Example 6.7.1 6.7. 1. Sometimes we want to prove that P ⇏ Q; P ⇏ Q; i.e. that P → Q P → Q is not a tautology. Recall. The equivalence. P → Q ⇔ (P ∧C1 → Q) ∧ ⋯ ∧ (P ∧Cm → Q) P → Q ⇔ ( P ∧ C 1 → Q) ∧ ⋯ ∧ ( P ∧ C m → Q) …
counter-example noun - Oxford English Dictionary
WEBFactsheet. What does the noun counter-example mean? There is one meaning in OED's entry for the noun counter-example. See ‘Meaning & use’ for definition, usage, and quotation evidence. See meaning & use. How common is the noun counter-example? …
Counter Definition & Meaning - Merriam-Webster
WEBMay 9, 2014 · 1. : a piece (as of metal or plastic) used in reckoning or in games. 2. : something of value in bargaining : asset. 3. : a level surface (such as a table, shelf or display case) over which transactions are conducted or food is served or on which …
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