Show that any tree with exactly two vertices of degree 1 is a path.
To show that any tree with exactly two vertices of degree 1 is a path, we can use a proof by contradiction.
Suppose we have a tree T with exactly two vertices of degree 1, but it is not a path. This means that there must be at least one vertex in the tree that has a degree greater than 1, because in a path, all vertices except the endpoints have a degree of 2, and there is no branching.
Now, let's consider a vertex v in the tree
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