Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose we have a finite collection of sets $A_1$,...,$A_n$. Is there an algorithm which gives a new collection $B_1$,...,$B_m$, which consist of pairwise disjoint sets, $\cup B_i=\cup A_j$ and each $B_i$ is a subset of some $A_j$?

share|cite|improve this question

1 Answer 1

up vote 7 down vote accepted

Write $B_k=A_k\setminus\bigcup_{j<k}A_j$. It might be the case that several of the sets will end up as being empty. Remove those.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.