A subset sum is a known to NP$-$hard problem. A decision version of the subset sum problem is$$defined as follows: Given a set X$[1...$n$]$ of positive integers and target integer T$,$ is there a subset$$of elements in X that add up to T$?$ Notice that there can be more than one such subset. For$$example$,$ if X $=\{8,6,7,5,3,10,9\}$ and T $=15,$ the answer is True, because the subsets $\{8,7\}$and $\{7,5,3\}$ and $\{6,9\}$ and $\{5,10\}$ all sum to $15.$ On the other hand, if X $=\{11,6,5,1,7,13,12\}$ and T $=15,$ the answer is False.$$a$.$ Design a brute force algorithm to solve this problem$$b$.$ Analyze the running time of the brute force algorithm$$c$.$ Do you think the decision version of the subset sum problem described above lend itself$$to the divide$/$decrease$/$transform and conquer algorithm design techniques? Support your$$answer with proper argument