수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 깨끗한 집합과 더러운 집합

delta 2019.11.13 08:26 조회 634

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

(선택공리 하)

공집합을 더러운 원소라고 하고 더러운 원소를 포함하는 집합을 더러운 집합이라고 하자.

더러운 원소를 포함하지 않는 집합은 깨끗한 집합이라고 한다.

또, 집합을 원소로 가지는 집합을 원소로 가지는 집합을 원소로 가지는 집합을 깊은 집합이라 하자.

예를 들어, $\{\{\{ \varnothing \} \}\}$ 는 깊은 집합이다.

문제1. $\{\{\varnothing \}\}$ 는 더러운 집합인가 깨끗한 집합인가?

문제2. 깊은 집합의 멱집합은 더러운 집합인가?

문제3. 더러운 집합 A와 깨끗한 집합 B의 교집합이 깊은 집합일때, A와 B의 합집합의 멱집합은 깊은 집합인가?

문제4. 모든 깨끗한 집합을 원소로 가지는 집합은 꺠끗한 집합인가?

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로보카폴리 Lv.11 2019.11.13 08:30 비밀댓글

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