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