Let E(n) be the statement that in a triangulation of a simple polygon with n sides, at least one of the triangles in the triangulation has two sides bordering the exterior of the polygon.
a) Explain where a proof using strong induction that E(n) is true for all integers n ≥ 4 runs into difficulties.
b) Show that we can prove that E(n) is true for all integers n ≥ 4 by proving by strong induction the stronger statement T (n) for all integers n ≥ 4, which states that in every triangulation of a simple polygon, at least two of the triangles in the triangulation have two sides bordering the exterior of the polygon.