How to determine if a statement is true

1. Jan 14, 2019

ver_mathstats

1. The problem statement, all variables and given/known data
Determine if the statement is true, n is a fixed positive integer.

If n is divisible by 6, then n is divisible by 9.

2. Relevant equations

3. 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?

2. Jan 14, 2019

LCKurtz

Yes. $12$ is another counterexample as is $30$. There are many.

3. Jan 14, 2019

ver_mathstats

Thank you very much.

4. Jan 14, 2019

Ray Vickson

Yes, any counterexample will do, as it shows the claimed statement to be false. A true statement cannot, ever, have any counterexamples!

5. Jan 14, 2019

ver_mathstats

Okay thank you very much, I understand now.