(a) Give a recursive definition of the set of Rooted Trees. (b) For a rooted tree T recursive definitions for v(T) and e(T) the number of vertices and edges of T respectively. (c) For a rooted tree T, use structural induction to prove that v(T) - e(T) = 1 (a) Give a recursive definition of the set of Rooted Trees. (b) For a rooted tree T recursive definitions for v(T) and e(T) the number of vertices and edges of T respectively. (c) For a rooted tree T, use structural induction to prove that v(T) - e(T) = 1