8-9.3

Part of 2018 239 Open Mathematical Olympiad

Problems(1)

All subsets into triples

Source: 239 Open MO, 2018, Junior League, Problem 3, Senior League, Problem 2

Is it possible to divide all non-empty subsets of a set of 10 elements into triples so that in each triple, two of the subsets do not intersect and in their union give the third? Proposed by Vladislav Frank