The map below shows the cities and one-way roads in Sikinia. (a) Prove that there is no closed path (a path is closed if it starts and quits in the same city) that visits every city exactly once. (b) Is there a closed path that visits every city exactly twice? (c) Is there a path, not necessary closed, that starts in the upper left corner and visits every city exactly once? (d) Is there a path, not necessarily closed, that starts in the upper left corner and visits every city exactly twice?