Consider set S and the power set $2^S$. The least upper bound of a subset X of $2^S$ is $\cup X$.
As any example, suppose $S=\{a,b,c\}$. Then consider $X=\{\{a,b\},\{c\}\}$ s.t. $X\subseteq 2^S$. Clearly, the least upper bound is the set $\{a,b,c\}$.
However, I am having difficulties proving this statement. Could anyone give me some pointers on how this can be done?