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 \(D(D(\mathcal F))=\mathcal F\).
The best solution was submitted by Jimin Park (박지민), 전산학과 2012학번. Congratulations!
Here is his solution of Problem 2014-21.
Alternative solutions were submitted by 박민재 (수리과학과 2011학번, +3), 채석주 (수리과학과 2013학번, +3), 이병학 (수리과학과 2013학번, +3), 정경훈 (서울대 컴퓨터공학과 2006학번, +3), 조현우 (경남과학고등학교 3학년, +3), 김경석 (경기과학고등학교 3학년, +3).