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Omni-MATH / Let S be a set of size 3. How many collections T of subsets of S have the property that for any two subsets U∈T and V∈T, both U∩V and U∪V are in T ?

Problem

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problem

Let SS be a set of size 3. How many collections TT of subsets of SS have the property that for any two subsets U∈TU \in T and V∈TV \in T, both U∩VU \cap V and U∪VU \cup V are in TT ?
Plain-text mathematical notation (without MathML)
Let S be a set of size 3. How many collections T of subsets of S have the property that for any two subsets U∈T and V∈T, both U∩V and U∪V are in T ?
Original LaTeX notation
Let $S$ be a set of size 3. How many collections $T$ of subsets of $S$ have the property that for any two subsets $U \in T$ and $V \in T$, both $U \cap V$ and $U \cup V$ are in $T$ ?

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Source and history

task_id
2755c304-be5b-5e94-b20d-9324f5ce507f
task_key
test--2755c304-be5b-5e94-b20d-9324f5ce507f
task_revision_id
1
config / split
/ test

Official source

initial import