Looking for a word for something whose inclusion implies the exclusion of another entity

I am looking for a word similar to “exclusive”, maybe is exactly this one, but I am confused by the fact that in my language (Spanish) there are two similar words that are used differently to express this nuance.

There is “exclusivo” (exclusive), which is used to express something that is limited or restricted to a certain group, for example: “an exclusive club”,

Then there is “excluyente”, which I don’t know if has a direct translation. It refers to something whose inclusion implies the exclusion of another entity, for example: “behaving as a particle or a wave are not mutually excluyentes in the mark of Quantum mechanics”, or “being at the park or at home at the same time are logically excluyentes“