functii
Scris: Vin Apr 03, 2015 11:41 pm
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
$\max_{f \in \mathcal{F}}| \textrm{Im}(f) |.$
Moldova TST 2015.
Let $n$ and $k$ be positive integers, and let be the sets $X=\{1,2,3,...,n\}$ and $Y=\{1,2,3,...,k\}$.
Let $P$ be the set of all the subsets of the set $X$. Find the number of functions $f: P \to Y$ that satisfy $f(A \cap B)=\min(f(A),f(B))$ for all $A,B \in P$.
$\max_{f \in \mathcal{F}}| \textrm{Im}(f) |.$
Moldova TST 2015.
Let $n$ and $k$ be positive integers, and let be the sets $X=\{1,2,3,...,n\}$ and $Y=\{1,2,3,...,k\}$.
Let $P$ be the set of all the subsets of the set $X$. Find the number of functions $f: P \to Y$ that satisfy $f(A \cap B)=\min(f(A),f(B))$ for all $A,B \in P$.