The independent set problem is defined in the textbook (Section 8.1)
as follows. In a graph G=(V,E), a set of nodes S is
independent if no two nodes in S are joined by an edge.
The decision problem is "Given a graph G and a number k,
does G contain an independent set of size at least k?"
The clique problem is as follows. In a graph G=(V,E), a set of
nodes S is called a clique if every pair of nodes in S
are joined by an edge.
The decision problem is "Given a graph G and a number k,
does G contain a clique of size at least k?"
 Prove that the clique problem is in NP. More specifically,
prove that, given a certificate corresponding to a subset
of nodes in G, it is possible to verify, in
polynomial time, that this subset is a clique
of G with size k.

The independent set problem is known to be NP complete.
(This is proven in Section 8.2 and 8.4 of the textbook.)
Prove that the clique problem is NP complete. More
specifically, prove that you may reduce a known NP complete problem
to the clique problem in polynomial time.