We define the problem INDEPENDENT SET as follows.

INDEPENDENT SET

Input: A graph \(\mathbf{G}\) and an integer \(k\).

Output: YES if there is a subset \(\mathbf{S}\) of the vertices in \(\mathbf{G}\) of size \(k\) or greater such that no edge connects any two vertices in \(\mathbf{S}\), and \(\mathrm{NO}\) otherwise.

Assuming that CLIQUE is \(\mathcal{N} \mathcal{P}\)-complete, prove that INDEPENDENT SET is \(\mathcal{N} \mathcal{P}\)-complete.