4 ms·
What am I not getting? Isn't family {1}, {2}, {3}, {4}, {1, 2, 3, 4} union-closed? Each element appears in only 2/5 of the sets, so ??? Edit: From the paper, t
by mgsouth 4y ago
What am I not getting? Isn't family {1}, {2}, {3}, {4}, {1, 2, 3, 4} union-closed? Each element appears in only 2/5 of the sets, so ???
Edit: From the paper, the family F is defined as "F ⊆ (subset or equal) 2^n". I think that means for n elements there are at most 2^n subsets? In other words, no duplicated subsets. Which still doesn't clear up my confusion--5 subsets is < 2^4.
Edit: Duh, thanks for correcting my thinko.
- nedhowley 4y ago"A collection, or family, of sets is considered “union-closed” if the union of any two sets in the family equals any existing set in the family." Your family isn't union closed because it doesn't include {1, 2}, the union of {1} and {2}.
- nimih 4y ago{1} U {2} = {1,2} and is not in the family.
- deleted 4y ago[deleted]