Let $S$ is a finite set with $n$ elements. We divided $AS$ to $m$ disjoint parts such that if $A$, $B$, $A \cup B$ are in the same part, then $A=B.$ Find the minimum value of $m$.
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Tags: combinatorics, Set systems, Enumeration
Let $S$ is a finite set with $n$ elements. We divided $AS$ to $m$ disjoint parts such that if $A$, $B$, $A \cup B$ are in the same part, then $A=B.$ Find the minimum value of $m$.