For every finite set XXX and every finite family of subsets A1,…,An⊆XA_1,\ldots,A_n\subseteq XA1,…,An⊆X, let I\mathcal{I}I be the set of distinct nonempty intersections ⋂i∈SAi\bigcap_{i\in S}A_i⋂i∈SAi for…