The floor plan of a fiveroom house is shown The rooms are la

The floor plan of a five-room house is shown. The rooms are labeled A, B, C, D, and E. The outside of the house is labeled F. The openings represent doors. Use the floor plan to answer the questions below. a. It is possible to draw a graph that models the connecting relationships on the floor plan, where vertices represent rooms and the outside and edges represent connecting doors. Choose the graph below that models the floor plan. b. Use the graph from part (a) to answer the following question. Is it possible to walk through each room and the outside, using each door exactly once? Yes No

Solution

a)

Step 1: Given, A, B, C, D, E are the rooms and F is the outside of the house

Step 2: Openings are the doors

Step 3: We have to draw a graph that models connecting relationship of the floor plan, where vertices represent rooms and outside and edges represent connecting doors

Step 4: Looking at the four graphs, the fourth graph models the floor plan because from the fourth graph

i) A to D is a door which is true if we look at the floor plan

ii) A to B is a door which is true if we look at the floor plan

iii) B to F is a door which is trues if we look at the floor plan

iv) B to C is a door which is true if we look at the floor plan

v) B to E is a door which is true if we look at the floor plan

vi) D to F is a door which is true if we look at the floor plan

Final Answer: Thus, the fourth graph models the floor plan

b)

Step 1: Using the graph from part (a), we need to go from

i) A to B, then

ii) B to E, then

iii) E to C, then

iv) C to B, then

v) B to F, then

vi) F to D

Final Answer: Yes, if we take the above path, we can walk through each room and the outside using each door exactly once