$6\mathrm{.}2$ A forest is a graph $($not necessarily connected$),$ each of whose components is a tree.

$($a$)$ Let $G$ be a forest with $n$ vertices and $k$ components. How many edges does $G$ have?

$($b$)$ Construct a forest with $12$ vertices and $9$ edges.

$($c$)$ Is it true that every forest with $k$ components has at least $2k$ vertices of degree $1?$