0
a conjecture is disproved if it is shown to be false. this can be done by providing a single concrete example (e.g. with actual numbers, functions, etc) that shows the conjecture's premise does not necessarily lead to its conclusion. alternatively, a conjecture could be shown to be false (i.e. disproved) by demonstrating that IF it were true then a logical consequence would be a clearly wrong statement (e.g. 2 + 2 =5)
Still curious? Ask our experts.
Chat with our AI personalities
Vivi
Beau
RafaAdd your answer:
Earn +20 pts
Is a case in which a conjecture is not true?
Counterexample
What is an example of a TRUE conjecture?
The Poincaré Conjecture.
What conjecture can you make about the sum of the first 10 positive even numbers?
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
Make a conjecture about the sum of the first 25 positive even numbers?
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
What is a conjecture about the number of factors for square numbers up to 1000?
One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.
