Q:

binary trees and rules for their creation

I am learning about binary trees. I was given following rules for their creation: A single leaf node is a binary tree. If t1 and t2 are binary trees, then the result of joining them under a single node is a binary tree. I suspect that the tree in the image is not a binary tree. My question is: How can I use the rules to prove that?

A:

Your rule should be amended to require that $t_1$ and $t_2$ are disjoint binary trees, i.e., they have no nodes in common. Then I trust the answer to your question becomes obvious.

