Which statements are correct?

  1. Only positive integers are categorized as prime and composite.
  2. Only positive integers are categorized as prime or composite.
  3. Only positive integers are categorized as either prime or composite.

I use the 2nd statement always but I think the third one is the most appropriate.

  • 1
    writing 'and/or' is a valid style and is in practice. I do it at times when both are correct. However, the last statement says integers could be ONLY one of them.
    – Maulik V
    Commented May 22, 2015 at 7:03
  • @Rohit But 1 is neither. Commented May 22, 2015 at 7:37
  • Linguistically, the original is fine. Mathematically 2 is necessary and sufficient.
    – AdamV
    Commented Dec 2, 2015 at 14:11

1 Answer 1


Really only 3 is precisely correct, since strictly speaking 2 allows (incorrectly) for a positive integer to be both prime and composite. That said, whether 2 is wrong kinda depends on the audience.

If you were talking to a group of maths students who clearly understood the mutually exclusivity of primeness and compositeness, and to whom you were stressing the point that neither term ever applies to negative integers, then 2 wouldn't cause too many issues.

But if you were talking to less experienced students, who hadn't yet grasped that primeness and compositeness were mutually exclusive, then it's better to play safe and use 3.

1 is, of course, simply wrong semantically.

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