$(20$ points$)$: Given the following list of edges in a directed graph:

$E=\{(A,B),(B,C),(C,D),(D,A),(C,E),(E,C)\},$

$($a$)$ Draw the directed graph.

$($b$)$ Identify any circuits within the graph. If any, classify them as simple or not.

$($c$)$ Does this graph have an Euler path or circuit? Justify your answer. Definition $($Euler Path$)$: An Euler

path in a graph is a path that uses every edge of the graph exactly once. If such a path exists, the graph

is said to be traversable. Note that an Euler path does not need to start and end at the same vertex. In con$-$

trast, an Euler Circuit is an Euler path which starts and ends on the same vertex, using every edge exactly once.