A complete graph is an undirected graph where each vertex is connected to every

other vertex by an edge. 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 given problem is NP$-$hard using Vertex Cover. Give more detail on the redcution process and proof of correctness.