91Ó°ÊÓ

What is the minimal element of the set of all subsets of a given set \(X\), partially ordered by set inclusion. What is the maximal element?

By the greatest lower bound of two elements \(a\) and \(b\) of a partially ordered set \(M\), we mean an element \(c \in M\) such that \(c \leqslant \mathrm{a}, c \leqslant b\) and there is no element \(d \in \mathrm{M}\) such that \(c