Exercise $1$: Consider the simple $($undirected$)$ graphs $P_5$ and $C_5.$ An orientation of an undirected

graph assigns to each edge a direction and thus creates a digraph.

$($a$)$ Provide an orientation of $P_5$ in which the resulting digraph is a path.

$($b$)$ Provide an orientation of $P_5$ in which the resulting digraph is not a path.

$($c$)$ Provide an orientation of $C_5$ in which the resulting digraph is a cycle.

$($d$)$ Provide an orientation of $C_5$ in which the resulting digraph is not a cycle.