My understanding of relations is still very basic, so I apologize in advanced for the basic question, but if possible, I would really appreciate some help on this problem.
If we let $A = \{ \{1 \}, \{2 \}, \{4 \}, \{1, 2 \}, \{1, 4 \}, \{2, 4 \}, \{3, 4 \}, \{1, 3, 4 \}, \{2, 3, 4 \} \}$, then $(A,\subseteq )$ is a partially ordered set.
I understand that it is a poset since it is reflexive, antisymmetric, and transitive. What I would like help on is how I would go about writing the relation $\subseteq$ on $A$ as a set of ordered pairs, but I am lost on how to do so properly.
Does this mean $R$ is just $R = \{ \{1 \}, \{2 \}, \{4 \}, \{1, 2 \}, \{1, 4 \}, \{2, 4 \}, \{3, 4 \}, \{1, 3, 4 \}, \{2, 3, 4 \} , \emptyset, A \}$?
$R$ is a subset of $A\times A$, where every pair in $R$ is related by $\subseteq$. $A$ is a set of sets, and so $R$ is a set of pairs of sets.
In short, $R:=\{\langle X,Y\rangle\in A{\times}A: X\subseteq Y\}$
For example,
$$\langle\{1\},\{1,2\}\rangle\in R\\\langle\{1,2\},\{1,2\}\rangle\in R\\\vdots\\\text{et cetera}$$