Question 5 (1 point) Given the following steps in the modification on the Euler Inequality proof (Theorem below), put them in order. Theorem: If a graph G is planar where each region is bounded by at least 4 edges, then the number of vertices and number of edges must satisfy |E| 2|VI - 4 Remember the steps to writing a proof: 1. Write the statement in terms of A => B 2. Examine the definition of A 3. State any other results you know about A. Substituting this found inequality in Euler's formula we have 2 E > 41R1 = 4 E - 41V + 8 2 E 4 E - 41V + 8 41V - 8 2 2 E 21V - 4 2 E > Let G be a planar graph. Then, it must satisfy Euler's Formula: TRI = EL- + 2 Since each region is bounded by at least four edges, the sum of all the region's bounds is at least 4 times the total number of regions. (#edges bounding each region) > 4|R| When counting the number of edges bounding each regions, every edge is counted twice: once on each side of the edge. Therefore, the sum of the regions is equal to 2 times the number of edges. (#edges bounding each region) = 2|E| Therefore, using the previous step, we can conclude 2 E > 41RI Therefore, for any planar graph where each region is bounded by at least four edges, we can conclude it satisfies 2|V] - 4 > EO