Consider the problem of PARTITION: we are given a set of numbers (if you prefer, you may think of these as positive integers; however, that is not necessarily part of the problem statement). We want to answer the boolean question: is there a subset of these elements whose sum is exactly half of the total? (a) Prove that this problem is in NP. (b) Observe that we could decide this language by making a call to any correct algorithm for Subset Sum with parameter T = (1/2) Xi. Why does this not prove anything about the difficulty of this problem? (c) Prove that this problem is NP-complete.