# 6Committees of Set Families, and Relative Blocking Constructions in Posets

Let r be a rational number, 0 ≤ r < 1. Given a nonempty family := {A1, ..., Aα} of nonempty and pairwise distinct subsets of its finite ground set $V\left(A\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}:={\displaystyle {\cup}_{i-1}^{\alpha}{A}_{i}},$ an r-committee of is defined to be a subset B ⊆ S of a set S ⊇ V() such that

for each i ∈ [α]. Thus, a 0-committee of is nothing else ...

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