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

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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

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Yes. ##12## is another counterexample as is ##30##. There are many.
 
Yes. ##12## is another counterexample as is ##30##. There are many.
Thank you very much.
 

Ray Vickson

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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!
 
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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