The following is a version of the Independent Set Problem. You are given a graph G = (V, E) and an integer k. For this problem, we will call a set I c V strongly independent if, for any two nodes v, u e I, the edge (v, u) does not belong to E, and there is also no path of two edges from u to v, that is, there is no node w such that both (u, w) e E and (w, v) e E. The Strongly Independent Set Problem is to decide whether G has a strongly independent set of size at least k.
Prove that the Strongly Independent Set Problem is NP-complete.
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