The discussion revolves around determining the truth of a mathematical statement regarding divisibility. The statement in question asserts that if a positive integer n is divisible by 6, then it must also be divisible by 9.
Participants have acknowledged the use of counterexamples as a valid approach to refute the statement. There is a shared understanding that any counterexample effectively demonstrates the falsehood of the claim, although multiple interpretations of the statement's implications are being explored.
Some participants reiterate the importance of counterexamples in establishing the truth value of mathematical statements, emphasizing that a true statement cannot have counterexamples.
Thank you very much.LCKurtz said:Yes. ##12## is another counterexample as is ##30##. There are many.
Yes, any counterexample will do, as it shows the claimed statement to be false. A true statement cannot, ever, have any counterexamples!ver_mathstats said:Homework Statement
Determine if the statement is true, n is a fixed positive integer.
If n is divisible by 6, then n is divisible by 9.
Homework Equations
The Attempt at a Solution
I know this statement is false because 6 is divisible by 6, however not divisible by 9. I showed a counterexample, is that enough to demonstrate that it is a false statement?
Ray Vickson said:Yes, any counterexample will do, as it shows the claimed statement to be false. A true statement cannot, ever, have any counterexamples!