Exercise 11.

Let \(T\) be a rooted tree that contains vertices \(u\text{,}\) \(v\text{,}\) and \(w\) (among possibly others). Prove that if \(w\) is a descendant of both \(u\) and \(v\text{,}\) then \(u\) is a descendant of \(v\) or \(v\) is a descendant of \(u\text{.}\)