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Because that is what a conjecture is! It is a proposition that has to be checked out to see f it is
- always true, false or indeterminate,
- sometimes true, false or indeterminate,
- never true, false or indeterminate.
Once its nature has been decided then it is no longer a conjecture.
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Why only one counterexample is necessary to show that a conjecture is false?
To be true a Conjecture must be true for all cases.
What shows that a conjecture is false?
A conjecture should be testable. You test it and if it fails the test, it is a false conjecture.
What is a statement that shows conjecture is false?
A counter example is a statement that shows conjecture is false.
Explain why a conjecture may be true or false?
A conjecture is but an educated guess. While there might be some reason for the guess based on knowledge of a subject, it's still a guess.
What are the steps to writing an Indirect Proof in Geometry?
Identify the conjecture to be proven.Assume the opposite of the conclusion is true.Use direct reasoning to show that the assumption leads to a contradiction.Conclude that the assumption is false and hence that the original conjecture must be true.
