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  2. A counterexample is used to check the validity of an argument. Consider the following statement: If a food is a fruit, then it is an apple. Now, consider this statement: Mango is a food. It is a fruit, but it is not an apple. Therefore, the mango is the counterexample, thereby making the first statement invalid.
    www.cuemath.com/data/counterexample/
    What is an example of a counterexample? 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.
    heimduo.org/what-is-an-example-of-a-counterexam…
    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. 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…

    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…
     
  3. People also ask
    What is an example of a counterexample?A counterexample is a specific example for which a statement is untrue. The existence counterexample proves the statement is false, even if it is often, mostly, or almost entirely true. Counterexamples are incredibly important for logic, which is, in turn, important because it provides the foundation for almost all mathematics. This section covers:
    What is a counterexample to a mathematical statement?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, Identify the condition and conclusion of the statement.
    How do you identify a counterexample?Identifying counterexamples is a way to show that a mathematical statement is false. When identifying a counterexample, 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.
    What is a counterexample in logic?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.
     
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  5. WebCounterexample. A counterexample is used to check the validity of an argument. Consider the following statement: If a food is a fruit, then it is an apple. Now, consider this statement: Mango is a food. It is a fruit, but it is …

  6. WebNov 21, 2023 · To make a counterexample in math, first, find an example that satisfies the conditions of the theorem. Then, demonstrate that the example proves the opposite of the conclusion of the...

  7. 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.

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