I want to prove the following is a matroid.
Let $G$ be a graph and $U, V$ be two subsets of its vertices. Consider the set $\mathcal{J}$ on $V$ as, $\mathcal{J}=\{A \subseteq V$ : there exists non-overlapping paths from some vertices of $U$ to $A\}$ I just need the proof for exchange property, means if $A, B \in \mathcal{I}$ with $|A| < |B|$, then there exists an element $x \in B \setminus A$ such that $A \cup {x} \in \mathcal{I}$.
Thanks for you help