(a) (5 pts) Find a symmetric chain partition for the power set P([5]) of [5] := {1, 2, 3, 4, 5} under the partial order of set inclusion. (b) (5 pts) Find all maximal clusters (namely antichains) of ([5]). Explain by no more than THREE sentences that the found clusters are maximal. (c) (5 pts) Find all maximal chains and all minimal antichain partitions of P([5]). Explain by no more than THREE sentences that the found chains are maximal and the found antichain partitions are minimal. (d) (5 pts) Please mark the Möbius function values µ(a,x) near the vertices x on the Hasse diagram of the h 8 e d b a poset, where x = a, b, c, d, e, f, g, h.