\begin{definition}[Definition:Depends Relation (Matroid)]
Let $M = \struct{S, \mathscr I}$ be a matroid.
Let $\rho : \powerset S \to \Z$ be the rank function of $M$.
 
For $x \in S$ and $A \subseteq S$, $x$ is said to '''depend''' on $A$, denoted as $x \sim A$, {{iff}}:
:$\map \rho {A \cup \set x} = \map \rho A$
\end{definition}