On the existence of sets

Question

It is an important question whether mathematical objects in fact exist. Certainly, we can't locate them in the physical world. I want to know whether sets exist. If they in fact do not exist, then all the axioms of ZFC are either false or vacuous. So, how do we establish that sets exist in the first place?

Answer 1

All formulations of ZFC imply that at least one set exists, either by implicit semantic rules of first order logic or by stating it directly.