0
A counterexample is sufficient to prove that a conjecture is false?
Wiki User
∙ 14y ago
Yes.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
How can you prove that a conjecture is false?
Give a counter-example.
How is testing a conjecture like finding a statement true or falsehow is it different?
well.......Its like testing a conjecture and finding a statement true or false because u have to test it!!! to see if its true or false and its different,true is like something u can prove and false is untrue and u cant prove it. :D i know i don't make sense but that's how i explained it on my homeworklol
What is a counterexample in math?
A counterexample is an example (usually of a number) that disproves a statement. When seeking to prove or disprove something, if a counter example is found then the statement is not true over all cases. Here's a basic and rather trivial example. I could say "There is no number greater than one million". Then you could say, "No! Take 1000001 for example". Because that one number is greater than one million my statement is false, and in that case 1000001 serves as a counterexample. In any situation, an example of why something fails is called a counterexample.
Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?
Yes - if such a counterexample can be found. However, using only the Euclidean axioms and logical arguments, it can be proven that the angles of a triangle in a Euclidean plane must add to 180 degrees. Consequently, a counterexample within this geometry cannot exist.
Why is AAA not an appropriate conjecture for triangle congruence?
It does not necessarily prove congruence but it does prove similarity. You can have a smaller or bigger triangle that has the same interior angles.
How can you prove that a conjecture is wrong?
Find one counterexample to negate the statement
How do you prove a conjecture is false?
Prove that if it were true then there must be a contradiction.
How can you prove that a conjecture is false?
Give a counter-example.
How can you prove that a conjecture is false in Geometry?
by bringing evidence to the table
How many examples to prove a conjecture false?
A counter example
How many counterexamples are required to prove that a conjecture is false?
One is enough.
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.
How is testing a conjecture like finding a statement true or falsehow is it different?
well.......Its like testing a conjecture and finding a statement true or false because u have to test it!!! to see if its true or false and its different,true is like something u can prove and false is untrue and u cant prove it. :D i know i don't make sense but that's how i explained it on my homeworklol
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.
To establish the validity of a conjecture is to?
prove it
Which type of reasoning is used to prove a conjecture?
scientific
What is a counterexample in math?
A counterexample is an example (usually of a number) that disproves a statement. When seeking to prove or disprove something, if a counter example is found then the statement is not true over all cases. Here's a basic and rather trivial example. I could say "There is no number greater than one million". Then you could say, "No! Take 1000001 for example". Because that one number is greater than one million my statement is false, and in that case 1000001 serves as a counterexample. In any situation, an example of why something fails is called a counterexample.
