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How to determine if a statement is true

  1. Jan 14, 2019 #1
    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. jcsd
  3. Jan 14, 2019 #2


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    Yes. ##12## is another counterexample as is ##30##. There are many.
  4. Jan 14, 2019 #3
    Thank you very much.
  5. Jan 14, 2019 #4

    Ray Vickson

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    Yes, any counterexample will do, as it shows the claimed statement to be false. A true statement cannot, ever, have any counterexamples!
  6. Jan 14, 2019 #5
    Okay thank you very much, I understand now.
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