Problem
1. Draw all the (a) free trees, (b) rooted trees, and (c) ordered trees with five vertices.
2. We can define the preorder traversal of an orchard as follows: If the orchard is empty, do nothing. Otherwise, first visit the root of the first tree, then traverse the orchard of subtrees of the first tree in preorder, and then traverse the orchard of remaining trees in preorder. Prove that preorder traversal of an orchard and preorder traversal of the corresponding binary tree will visit the vertices in the same order.