Prove or disprove: (a) For every tree T with at least two vertices, the number of leaves of T is at least two more than the number of vertices of degree at least 3 in T. (b) Every graph with n vertices has at most n - 1 bridges. (c) Let G be a graph and let e and f be distinct bridges of G. Then e is a bridge of G' = G\{f}. (d) Let G be a graph and let f be a bridge of G. Let e be a bridge of G' =G\{f}. Then e is a bridge of G. (e) If G has exactly one spanning subgraph H such that H is a tree, then G is a tree. Prove or disprove: (a) For every tree T with at least two vertices, the number of leaves of T is at least two more than the number of vertices of degree at least 3 in T. (b) Every graph with n vertices has at most n - 1 bridges. (c) Let G be a graph and let e and f be distinct bridges of G. Then e is a bridge of G' = G\{f}. (d) Let G be a graph and let f be a bridge of G. Let e be a bridge of G' =G\{f}. Then e is a bridge of G. (e) If G has exactly one spanning subgraph H such that H is a tree, then G is a tree