Consider a complete graph G $=($V$,$ E$)$ with n vertices, where an edge

weight we is defined on each edge. As additional input, you are given two positive integers k

and W$.$ Consider the following problem: given these inputs, is there a set of vertices of size

k such that for each pair of vertices in this set, the edge connecting them has weight at least W$?$ Prove that this problem is NP$-$complete using $3-$SAT