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Difference between revisions of "2006 Romanian NMO Problems/Grade 10/Problem 1"

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*[[2006 Romanian NMO Problems/Grade 9/Problem 1 | Previous problem]]
 
*[[2006 Romanian NMO Problems/Grade 9/Problem 3 | Next problem]]
 
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[[Category:Olympiad Geometry Problems]]
 
[[Category:Olympiad Geometry Problems]]

Revision as of 15:03, 7 May 2012

Problem

Let $M$ be a set composed of $n$ elements and let $\mathcal P (M)$ be its power set. Find all functions $f : \mathcal P (M) \to \{ 0,1,2,\ldots,n \}$ that have the properties

(a) $f(A) \neq 0$, for $A \neq \phi$;

(b) $f \left( A \cup B \right) = f \left( A \cap B \right) + f \left( A \Delta B \right)$, for all $A,B \in \mathcal P (M)$, where $A \Delta B = \left( A \cup B \right) \backslash \left( A \cap B \right)$.

Solution

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See Also

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