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To be true a Conjecture must be true for all cases.

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Q: Why only one counterexample is necessary to show that a conjecture is false?
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What number would be a counterexample to the following conjecture Prime numbers are odd?

2 would be a counterexample to the conjecture that prime numbers are odd. 2 is a prime number but it is the only even prime number.


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How can you prove a conjecture false?

The word "conjecture" can be taken a number of ways. If the "conjecture" involves an inference based on false or defective information, you need only show convincing or conclusive evidence that the information is false or faulty. If the "conjecture" is the result of surmise or guessing, then it is nothing more than a guess itself, and, therefore, has no basis in fact or logic. If the "conjecture" is an unproven mathematical hypothesis, you will need to disprove its validity from its basis. Start with the basic crux of the problem and work step by step until you disprove (or prove) the hypothesis to be untrue (or true). Make sure you have good arguments and sound mathematics.


How is testing a conjecture different from finding a statement true or false?

There are only two possible outcomes in finding out whether a statement is true or false.In testing a conjecture, even one contradiction is sufficient to disprove it. However, it can never be proven. All you can do is add support to the likelihood that the conjecture is true. But there remains a possibility that some other test will prove it false.Furthermore, in view of Godel's incompleteness theorem, some conjectures cannot be proven to be true even if you can prove that their negation is false.


Is this statement true if the product of two integers is divisible by 6 one of the integers is also divisible by 6?

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Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?

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A number is divisible by 6 if and only if it is divisible by 3?

If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6. It becomes clearer if you split the question into its two parts. A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. A number is divisible by 6 only if it is divisible by 3? True.


True or False special handling for all sensitive data including PHI requires accessing only what is necessary to complete a work related duty or job this is known as the minimum necessary rule?

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