# 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.

## 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?

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.

Homework Helper
Dearly Missed

## 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.

## 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.