Final answer:
The statement is FALSE. The relationship between an independent set and a clique in graph theory is not straightforward; they represent opposite concepts and adding a clique doesn't guarantee a solution for an independent set problem.
Step-by-step explanation:
The question pertains to the concepts of independent sets and cliques within the context of graph theory, which is a field of mathematics. In the independent set problem, we search for the largest set of vertices in a graph such that no two vertices are adjacent. If there is an independent set, adding the complementary set as a clique does not guarantee a forced solution, because the properties that define an independent set and a clique are opposites.
In simpler terms, a clique in a graph is a subset of vertices with an edge between every pair (every vertex is connected to every other vertex in the clique), while an independent set is a group of vertices where no two vertices are connected by an edge. Because of this dichotomy, the relationship between a clique and an independent set is not as straightforward as the question might suggest. In fact, in the context of the NP-complete problem, they represent two different challenges. Thus, the implication that adding a clique would force a solution in the independent set problem is false.