How to determine if a statement is true

[ver_mathstats]

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?

 

[LCKurtz]

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

 

[ver_mathstats]

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

Thank you very much.

 

[Ray Vickson]

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?

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

 

[ver_mathstats]

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

Okay thank you very much, I understand now.