Let $G = (V, E)$ be an undirected graph. A subset $I \subseteq V$ of the vertices in $G$ is an independent set if no two vertices $u, v \in I$ are adjacent in $G$, i.e., for any $u, v \in I$, we have $(u, v) \not \in E$.
Define the Independent Set Problem (IS) to take as input a graph $G$ and an integer $k$ and determine whether $G$ contains an independent set $I$ with $|I| \ge k$. Show that the IS is NP-complete by proving $3SAT \le_p IS$.