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Omni-MATH / Let F be the set of all the functions f : mathcal{P}(S) longrightarrow mathbb{R} such that for all X,Y⊆S, we have f(X∩Y)=min(f(X),f(Y)), where S is a finite set (and P(S) is the se…

Problem

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problem

Let F\mathcal{F} be the set of all the functions $f : \mathcal{P}(S) \longrightarrow \mathbb{R}$ such that for all X,Y⊆SX, Y \subseteq S, we have f(X∩Y)=min(f(X),f(Y))f(X \cap Y) = \min (f(X), f(Y)), where SS is a finite set (and P(S)\mathcal{P}(S) is the set of its subsets). Find \[\max_{f \in \mathcal{F}}| \textrm{Im}(f) |. \]
Plain-text mathematical notation (without MathML)
Let F be the set of all the functions $f : \mathcal{P}(S) \longrightarrow \mathbb{R}$ such that for all X,Y⊆S, we have f(X∩Y)=min(f(X),f(Y)), where S is a finite set (and P(S) is the set of its subsets). Find
\[\max_{f \in \mathcal{F}}| \textrm{Im}(f) |. \]
Original LaTeX notation
Let $\mathcal{F}$ be the set of all the functions $f : \mathcal{P}(S) \longrightarrow \mathbb{R}$ such that for all $X, Y \subseteq S$, we have $f(X \cap Y) = \min (f(X), f(Y))$, where $S$ is a finite set (and $\mathcal{P}(S)$ is the set of its subsets). Find
\[\max_{f \in \mathcal{F}}| \textrm{Im}(f) |. \]

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Source and history

task_id
72ee1b58-15f6-5c16-80a4-41a04bafd44e
task_key
test--72ee1b58-15f6-5c16-80a4-41a04bafd44e
task_revision_id
1
config / split
/ test

Official source

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