John Baez #10 Thanks for the explanation. Since \\( X\\) is the smallest element such that \\(A \le X\\) and \\(B \le X\\). It follows that any \\(C\\) for which \\(A \le C\\) and \\(B \le C\\), \\(\implies\\) \\(C \geq X\\), i.e. \\(C\\) is at least the same as \\(X\\) or is the union of \\(X\\) and another set.