Write a formal statement(with quantifiers) expressing the idea that "if two natural numbers' products is 3, then one of those numbers is 1"

I have (x in N) (y in N) [(xy=3) - (x = 1 v y = 1)]
but doesn't the or make it so both can be true?
What would be the correct way of writing it?

Question

Write a formal statement(with quantifiers) expressing the idea that "if two natural numbers' products is 3, then one of those numbers is 1"


I have  (x in N) (y in N) [(xy=3) -> (x = 1 v y = 1)]
but doesn't the or make it so both can be true?
What would be the correct way of writing it?

debbieg · Answer

I get what you're saying, but I don't think it's a problem. What I mean is, the or means that at least one or the other is true, which is all that you need to say. In general, yes, an "or" means that both MIGHT be true, but it doesn't mean that both MUST be true. 

Now, if you were asked to express that "EXACTLY one of those numbers is 1", then you would have to tweak it, but that isn't what was asked (as I read it).

debbieg · Answer

But if you WANT to specify that it is only 1, then you can just make the statement on each side of the or a compound statement: $\large x=1 ~and~ y\neq 1$ or.... etc.