Question: Let X be a set and let S be a collection of subsets of X (ie. S is a subset of the power set

Let X be a set and let S be a collection of subsets of X (ie. S is a subset of the power set P(X)). Then S is

Let X be a set and let S be a collection of subsets of X (ie. S is a subset of the power set P(X)). Then S is partially ordered by the subset relation C. Suppose that (S.C) is also linearly ordered, meaning that for all A, B E S cither ACB or BCA. Prove that S = {X-A|A E S} is also linearly ordered by C.

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