1. What is the next line of the proof? a). Assume the theorem holds for all graphs with k edges. b). Let G be a graph with k edges. c). Assume the theorem holds for all graphs with k+1 edges. d). Let G be a graph with k+1 edges. e). Assume the theorem holds for all graphs with k-1 edges. f). Let G be a graph with k-1 edges.

2. What is the next line of the proof? a). Let G be a graph with k edges. b). Assume the theorem holds for all graphs with k+1 edges. c). Let G be a graph with k+1 edges. d). Assume the theorem holds for all graphs with k-1 edges. e). Let G be a graph with k-1 edges.

3. What is the next line of the proof? a). Add a vertex to G to create G’. b). Delete a vertex from G to create G’. c). Add an edge to G to create G’. d). Delete an edge from G to create G’.

4. Is the graph shown maximal planar? a). Yes b). No c). I have absolutely no idea

5. Is the graph shown planar? a). Yes b). No c). I have absolutely no idea

6. Is the graph shown maximal planar? a). Yes b). No c). I have absolutely no idea

7. How many regions does the given graph have? a). 0 b). 4 c). 5 d). 6 e). 7 f). 8 g). 9 h). 10 i). 11 j). 12

8. Is the graph shown maximal planar? a). Yes b). No c). I have absolutely no idea

9. What is the next line of the proof? a). Assume G has a vertex of degree  5. b). Assume G has two vertices of degree  5. c). Assume all vertices in G have degree  5. d). Assume G has a vertex of degree  6. e). Assume all vertices in G have degree  6.

10. What is the next line of the proof? a). 2q = 6p. b). 2q = 6r c). 2q  6pd). 2q  6r e). 2q  6pf). 2q  6r