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Say we have a finite collection ## S_1,...,S_n ## of sets , which are not all pairwise disjoint , and we want

to find the minimal collection of the ## S_j ## whose union is ## \cup S_j ## . Is there

any theorem, result to this effect?

I would imagine that making the ## S_j## pairwise-disjoint would help. Is there some other way?

I think I remember some results about results elated to minimal systems of representatives, maybe would also work?

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# "Minimal Cover" in Finite Collection of Sets?

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