I can't really figure it out how to solve the following exercise:
Let $X$ be a set and $Y$ a subset of $X$ containing at least two distinct elements. Let's consider the partially ordered set $2^X$ ordered by inclusion and define $B=\{\{y\}\space y\in Y\}$ and $Z$ being a fixed subset of $2^X$, prove:
1) $Z$ is a majorant of $B$ iff $Y$ is contained in $Z$,
2) $Z$ is a minor ant of $B$ iff $Z$ is the empty set,
3) what are (if they exist) $\sup B$ and $\inf B$.
I can't figure what exactly the exercise is asking to me so I'd like a step by step solution.