## Disjoint Union of Cycles

Let G be a graph, $u, v \epsilon V(G)$ two distinct vertices, and $p_{1}$ and $p_{2}$ two different u, v-paths. Viewing these graphs as subgraphs of G, show that $p_{1} \triangle p_{2}$ constitutes a disjoint union of cycles in G. Does the same hold for digraphs?