# Let E(n) be the statement that in a triangulation of a ## Problem 23E Chapter 5.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 23E

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.

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##### ISBN: 9780073383095

Since the solution to 23E from 5.2 chapter was answered, more than 371 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 23E from chapter: 5.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “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.” is broken down into a number of easy to follow steps, and 113 words. This full solution covers the following key subjects: Triangulation, polygon, Sides, integers, exterior. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th.

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