Geodesic
Orthogonal Families of Sets
Canadian mathematical bulletin, Tome 14 (1971) no. 4, p. 573

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DOI

In this note we answer in the affirmative the following question. If S is a finite family of sets such that each subset of a member of S also belongs to S, is it possible to arrange the sets in pairs so that the first member of the pair is contained in the complement of the second member? 
Marica, John. Orthogonal Families of Sets. Canadian mathematical bulletin, Tome 14 (1971) no. 4, p. 573. doi: 10.4153/CMB-1971-104-6
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     title = {Orthogonal {Families} of {Sets}},
     journal = {Canadian mathematical bulletin},
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     year = {1971},
     volume = {14},
     number = {4},
     doi = {10.4153/CMB-1971-104-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-104-6/}
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