7. (8 marks) Let n be a positive integer, and consider a drawing consisting of n dots such that each pair of distinct dots is connected by a line and there is an arrowhead on each line pointing in one direction or the other. An example with five dots labelled A, B, C, D, and E is shown below. Prove by induction that, no matter how the arrows are directed, it is possible to to construct a path that includes each dot exactly once by starting at some dot and following lines in the directions indicated by the arrows. Two such paths in the example below are A, C, E, B, D and A, B,C, E, D. The path C, E, A, B, D does not satisfy the requirements because the line between E and A goes in the wrong direction