\begin{itemize}

	\item Question: Use the known {\it NP-Completeness} of {\bf
	SATISFIABILITY} to show that some other problem is {\it
	NP-Complete}

	\item Answer:
	INSTANCE:
	Given a graph G, does it have a clique of size k?

	SOLUTION:
	reduce 3-SAT to CLIQUE as follows: for each member of the list
	of variables(?) in the 3-SAT problem  create a vertex. Join
	each vertex with every other vertex as long as the following is
	true, the verticies are in different groups (from 3-SAT groups,
	or clauses) and the verticies are "consistent"(?) (ie, a and a'
	cannot go together)

	This construction can obviously be done in polynomial time.
	The question to be answered is this: with the graph constructed
	as such, is there a clique of size k, where k is the number of
	clauses (or groups) from 3-SAT.  If so then there is a solution
	for 3-SAT, and it is the assignment that each vertex has that
	is in the clique.  

\end{itemize}
