Proof by induction.

I. Initial condition. Let T be a tree with 2 vertices. Then T has two vertices of degree 1, by definition of tree (connected graph without cycles).

II: Rule of induction. Let b U be a tree with n, and addume that U has at least 2...

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Proof by induction.

I. Initial condition. Let T be a tree with 2 vertices. Then T has two vertices of degree 1, by definition of tree (connected graph without cycles).

II: Rule of induction. Let b U be a tree with n, and addume that U has at least 2 vertices of degree 1. Adding another vertex will either (i) maintain the number of vertices of degree 1 (by connecting to a vertex of degree one) or (ii) increase the number of vertices of degree 1 (by connecting to a vertex of degree greater than 1).

Taking I and II together means that any tree with 2 or more vertices will contain at least two vertices of degree 1. QED