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A counterexample is sufficient to prove that a conjecture is false?
Yes.
Can a theorem have a counterexample?
No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
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.
How determine whether the conjecture is true or false. If false give a counterexample. Given LMN and XMZ are coplanar. Conjecture The angles are vertical angles.?
Select one: a. False; the angles may be supplementary. b. True c. False; one angle may be in the interior of the other. d. False; the angles may be adjacent.
How many Counterexamples are needed to disprove the conjecture two lines in a plane always intersect at exactly one point?
To disprove the conjecture that two lines in a plane always intersect at exactly one point, only one counterexample is needed. A single example of two lines that do not intersect, such as two parallel lines, is sufficient to show that the conjecture is false. Therefore, one counterexample is enough to invalidate the claim.
Any number that is divisible by 2 is also divisible by 6 Find a counterexample to show that the conjecture is false?
4 is divisible by 2 but not by 6
Any number that is divisible by 3 is also divisible by 9 .Find a counterexample to show that the conjecture is false?
You are an Idiot dude. there is no such value
A counterexample is sufficient to prove that a conjecture is false?
Yes.
What is an example that shows a conjecture is false?
It's a counterexample.
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.
Why only one counterexample is necessary to show that a conjecture is false?
To be true a Conjecture must be true for all cases.
Conjecture Any number that is divisible by 4 is also divisible by 8?
False. Consider 4, itself.
Which counterexample shows that the conjecture All mammals are monkeys is false?
A mouse is a mammal, but it us not a monkey.
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.
Find a counterexample to show that the conjecture is false?
if the qoutient of two numbers is positive, then both numbers must be a rectangle.
Can a theorem have a counterexample?
No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
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.
