# 2014-21 Duality

Let $$\mathcal F$$ be a non-empty collection of subsets of a finite set $$U$$. Let $$D(\mathcal F)$$  be the collection of subsets of $$U$$ that are subsets of an odd number of members of $$\mathcal F$$. Prove that $$D(D(\mathcal F))=\mathcal F$$.

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