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What number would be a counter example to the following conjecture. Prime numbers are odd?
Wiki User
∙ 12y ago
The number 2 is even as well as prime.
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∙ 12y ago
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What conjecture can you make about the sum of the first 46 positive odd numbers?
Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all). One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less. A sensible conjecture might be that the sum is odd. This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).
What is a conjecture about the product of 2 odd numbers?
Their product will also be an odd number.
What is a counter example for the statement that all odd numbers are prime?
9 = 3 x 3 15 = 3 x 5 etc. Any odd number that is composite. But 2 is a prime number which is not an odd number. [Wrong question: that is a counter example to all primes are odd numbers]
What numbers as a sum of two prime numbers 95?
You can't write that as the sum of two prime numbers. Note: Goldbach's Conjecture (for expressing numbers as the sum of two prime numbers) applies to EVEN numbers.
What are numbers that have exactly 4 factors?
Those numbers would have to have following forms of prime factors:a3, where a is any prime number. For example, 23 = 8.ab, where a and b are two different prime numbers. For example, 2 x 3 = 6.
What number would be a counterexample to the following conjecture Prime numbers are odd?
2 would be a counterexample to the conjecture that prime numbers are odd. 2 is a prime number but it is the only even prime number.
Find a counter example to show that the following The sum of any two odd numbers is divisible by 4?
3+3=6 which is clearly not divisble by 4
Write a conjecture about the product of two odd numbers?
My conjecture (an opinion based on incomplete information) is that the product of two odd numbers is 22. There is no requirement for a conjecture to be true.
Conjecture about the sum of the first 30 positive even numbers?
There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
What is a counter example?
A counter example occurs when somebody makes a claim that all members of some category of things have a particular property, and then someone else proves that the claim is not true by showing an example of a thing in the category that does not have the property claimed. For example, if someone claimed that "All presidents of the United States are dead white men", then Barack Obama would be a counter-example because he is a president of the United States but isn't a dead white man. For another example, if someone claimed that all mammals bear live young, the echidna and the platypus would be counter-examples because they are mammals that lay eggs. For another example, if someone claimed that the United States is the only country that has never defaulted on its debts, Australia and Tuvalu would be counter-examples. The claim is logically equivalent to saying that all countries in the category of being not the USA have defaulted on a debt at least once,.... For another example, if someone claimed that all prime numbers are odd, "2" would be a counter example. Or if someone claimed that all odd numbers are prime "9" would be a counter-example. In short, a counter-example to a proposition or claim is an example that proves that the proposition or claim is not true.
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.
What is the conjecture of the sum of the first 100 positive even numbers?
You do not need a conjecture; you can calculate the answer. The answer is 10,100
What is counter example?
A counter example is a proof of a negation of a universal statement.A statement of the form "all X are Y" (e.g. all men are mortal), can be disproved by providing a counter example (here: something (someone) which is both a man and immortal).A more mathematical example of the use of a counter example could be to disprove the statement "the product of two prime numbers is odd". This is a claim about all numbers which are the product of two prime numbers (all elements in the set {n in N | n = p*q where p and q are prime numbers}). This set contains infinitely many pair numbers, but a single example (or witness), is enough to disprove the statement. Four is such a number and can serve as a counter example.
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.
What disproves a conjecture?
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)
If the product of two numbers is even then do the two numbers both have to be positive?
No. Counter Example: -2 * -2 = 4
What is the conjecture that states that all even numbers over 2 can be expressed as the sum of two primes?
Goldbach's conjecture
