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Omni-MATH / Find the number of nonempty sets F of subsets of the set {1,…,2014} such that: (a) For any subsets S₁,S₂∈F,S₁∩S₂∈F. (b) If S∈F,T⊆{1,…,2014}, and S⊆T, then T∈F.

Problem

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problem

Find the number of nonempty sets F\mathcal{F} of subsets of the set {1,…,2014}\{1, \ldots, 2014\} such that: (a) For any subsets S1,S2∈F,S1∩S2∈FS_{1}, S_{2} \in \mathcal{F}, S_{1} \cap S_{2} \in \mathcal{F}. (b) If S∈F,T⊆{1,…,2014}S \in \mathcal{F}, T \subseteq\{1, \ldots, 2014\}, and S⊆TS \subseteq T, then T∈FT \in \mathcal{F}.
Plain-text mathematical notation (without MathML)
Find the number of nonempty sets F of subsets of the set {1,…,2014} such that: (a) For any subsets S₁,S₂∈F,S₁∩S₂∈F. (b) If S∈F,T⊆{1,…,2014}, and S⊆T, then T∈F.
Original LaTeX notation
Find the number of nonempty sets $\mathcal{F}$ of subsets of the set $\{1, \ldots, 2014\}$ such that: (a) For any subsets $S_{1}, S_{2} \in \mathcal{F}, S_{1} \cap S_{2} \in \mathcal{F}$. (b) If $S \in \mathcal{F}, T \subseteq\{1, \ldots, 2014\}$, and $S \subseteq T$, then $T \in \mathcal{F}$.

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Source and history

task_id
459e571d-f473-5a8b-bbeb-cc54e51c3402
task_key
test--459e571d-f473-5a8b-bbeb-cc54e51c3402
task_revision_id
1
config / split
/ test

Official source

initial import