Hi, to everybody. I find it really disconcerting that when it comes to a question the colleagues vote negative my own question made and proposed with clarity. I would like to invite so many colleagues and users to be much more professional and humble. Hi to all.

Hi

@user193319 I guess singletons could give a counterexample...?

At least for finite unions you should be able to say something" Convex hull of finite union and Convex hull of the union of two nonempty sets.

This is also related: How to prove that $H(S_1\cap S_2)\subset H(S_1) \cap H(S_2)$ and $H(S_1 \cup S_2) \supset H(S_1) \cup H(S_2)$