# How to determine if a statement is true (1 Viewer)

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#### 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?

#### LCKurtz

Homework Helper
Gold Member
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 Helper
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?
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.

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