Meaning of "Any two deterministic quantities are independent"

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I'm having trouble understanding this statement: "any two deterministic quantities are independent"

The example the text provides is as follows: $$Prob(\varnothing\cap\Omega) = Prob(\varnothing) = 0 = Prob(\varnothing)P(\Omega) $$ Which proves $\varnothing$ and $\Omega$ are independent.

However, we cannot say that any event A and its complement, $A^C$, is necessarily independent(at least I don't think). My question is why are two deterministic quantities are independent? (Maybe I'm just not understanding what deterministic in this context means?)

Any guidance is greatly appreciated :)