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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.
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 is testing a conjecture like finding a stament true or false?
Testing a conjecture is similar to determining the truth value of a statement because both involve evaluating evidence to establish validity. In mathematics, a conjecture is an unproven assertion that requires either proof or a counterexample. When testing a conjecture, one seeks to demonstrate it as true by finding cases that support it or to disprove it by identifying a single counterexample. Thus, both processes rely on logical reasoning and empirical investigation to confirm or refute claims.
Is it true or false that a number is divisible by 6 if and only if it is divisible by 3?
False. The question consists of 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? This is true but the false part makes the whole statement false.
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.
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.
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.
Which counterexample shows that the conjecture Every four-sided figure is a parallelogram is false?
Every four sided figure is a quadrilateral which includes a parallelogram.
