c) Consider the ordered set $(\mathbb{N}, |)$, where $|$ is the relation divides on $\mathbb{N}$. Let $A = \{2, 3, 4, 5, 9, 12\}$. Find all the minimal, maximal, minimum, maximum, infimum and supremum elements of A if they exists.
Question 4.
Let $X = \{4, 6, 8, 9\}$. Consider the ordered set $(P(X), \subseteq)$.
a) Is $P(X)$ a chain?
b) Give any three maximal chains of $P(X)$.
c) Does $P(X)$ have a supremum and an infimum? If so, give them.