[thaumasiotes]

> The argument in the article is the following:

This is incorrect. You attribute an argument to the article that it does not make.

> This argument is valid only if A ⋂ B ≠ ∅

This is vacuously true in that the argument is not valid and its validity therefore implies all propositions including that A ⋂ B ≠ ∅. Although I tend to suspect that that isn't what you meant to say. It is equally true that "This argument is valid only if A ⋂ B = ∅". It is not true that if a function f takes a constant value, you can conclude that A ⋂ B ≠ ∅ for arbitrary A and B.

[poetically]

Great, glad we cleared that up.