Drag and drop the recursive definitions against their corresponding sets.

Rooted tree

Rooted tree drop zone empty.

Extended binary tree

Extended binary tree drop zone empty.

Full binary tree

Full binary tree drop zone empty.

Basis step: A single vertex r is a rooted tree

Recursive step: Suppose that T$1,$T$2,...,$ Tn are disjoint rooted trees with roots r$1,$r$2,...,$ rn$,$ respectively. Then the graph formed by starting with a root r$,$ which is not in any of the rooted trees T$1,$T$2,...,$ Tn$,$ and adding an edge r to each of the vertices r$1,$r$2,...,$ rn$,$ is also a rooted tree.

Basis step: The empty set is an extended binary tree

Recursive step: If T$1$ and T$2$ are disjoint extended binary trees, there is an extended binary tree, denoted by T$1$ T$2,$ consisting of a root r together with edges connecting the root to each of the roots of the left subtree T$1$ and the right subtree T$2$ when these trees are nonempty.

Basis step: There is a full binary tree consisting only of a single vertex.

Recursive step: If T$1$ and T$2$ are disjoint full binary trees, there is a full binary tree, denoted by T$1$ T$2,$ consisting of a root r together with edges connecting the root to each of the roots of the left subtree T$1$ and the right subtree T$2.$