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What is needed to show that a conjucture is false?

To show that a conjecture is false, one must provide a counterexample—an instance or case where the conjecture does not hold true. This counterexample must be specific and clearly demonstrate that the conjecture fails under certain conditions. Additionally, it's important to ensure that the counterexample is within the scope of the conjecture's claims to effectively disprove it.


Specific case in which a statement is false?

A counterexample is a specific case in which a statement is false.


What conjecture can you make about the sum of the first 46 positive odd numbers?

Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all). One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less. A sensible conjecture might be that the sum is odd. This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).


What is a case in which a conjecture is not true?

Counterexample


What is a counterexample to this conjecture if three lines lie in the same plane then they intersect in at least one point?

A counterexample to the conjecture is when three parallel lines lie in the same plane. In this case, none of the lines intersect at any point, demonstrating that it is possible for three lines in the same plane to not intersect at all. Therefore, the conjecture is proven false.


What kind of statement is a conjecture?

A conjecture is a statement that is believed to be true, but has yet to be proven. Conjectures can often be disproven by a counter example and are then referred to as false conjectures.


Is a case in which a conjecture is not true?

Counterexample


What structure of the female reproductive has malfunctioned in this case?

We'll be happy to conjecture if you'll describe the case. Deal ?


Is it true that in inductive reasoning you use a general rule to make a decision about a specific case?

false


Is a conjecture about the sum of two negative integers?

The sum of two negative numbers is 27.5 unless you add them together on a Tuesday, in which case the sum is 25.7. That is a conjecture about the sum of two negative numbers. There is no reason for a conjecture to be true, or even credible.


How do you use the ideas of counterexamples to verify valid conjectures and refute invalid conjectures?

Counterexamples are used to test the validity of conjectures by providing a specific instance where a conjecture fails. If a counterexample is found, it refutes the conjecture, demonstrating that it is invalid. Conversely, if no counterexamples can be found despite thorough testing, it supports the conjecture's validity, although this does not prove it universally true. Thus, while counterexamples are critical for refutation, their absence strengthens the case for a conjecture, though further proof may still be needed for confirmation.


How does the number 30 fit the goldbach's conjecture?

Goldbach's conjecture says that every even number greater than two can be expressed as the sum of 2 primes. If 30 could not be expressed as the sum of two primes, then this would disprove the conjecture. As it is, 30 can be expressed as the sum of two primes. You can express it as 11+19. Thus, Goldbach's conjecture holds in this case.