Draw an undirected tree and then attempt to do the following tasks. Conjecture which of these tasks are possible and which are impossible: (a) Draw a directed tree with the same number of vertices and...

Draw an undirected tree and then attempt to do the following tasks. Conjecture which of these tasks are possible and which are impossible:

(a) Draw a directed tree with the same number of vertices and edges.

(b) Draw a new undirected tree with the same number of vertices but a different number of edges.

(c) Add an edge to the tree without creating a cycle.

(d) Remove an edge from the tree without disconnecting any pair of vertices.