2. [4] In the proof of Dilworth's Theorem, the second case starts as follows. . P is a poset. C is a maximal chain in P. The width of P and of P-C are the same. A is a maximal antichain in P-C. S+ ={E P|≥a, for some a, € A}. S={E P|≤a, for some a, E A}. In the diagram below there is a poset P. The chain C is marked with dashed lines. The antichain A= (a1, a2, as) is indicated with the labelled red points. (a) Put a + beside all points in St. (b) Put a beside all points in S (c) Find an optimal chain decomposition of St. (d) Find an optimal chain decomposition of S