Consider the optimization problem MIN-VERTEX-COVER which takes a graph as an input and returns the smallest value k such that there is a vertex cover of the graph of size k. Compare this to the decision problem VERTEX-COVER which takes a graph mid an integer k as input and returns true if the graph has a vertex cover of size no more than k (or else returns false). Complete the following to show that (a) Explain Why MIN-VERTEX-COVER is at least as hard as VERTEX-COVER. Note, you will want to do something similar to a reduction here (in the correct direction), but since the outputs are of different types, you me really just showing how to solve one problem using an algorithm for the other. (b) Now go the other way: Explain why VERTEX-COVER is at least as hard as MIN-VERTEX-COVER