Difference between revisions of "2006 Romanian NMO Problems/Grade 10/Problem 1"
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==Problem== | ==Problem== | ||
| + | Let <math>M</math> be a set composed of <math>n</math> elements and let <math>\mathcal P (M)</math> be its power set. Find all functions <math>f : \mathcal P (M) \to \{ 0,1,2,\ldots,n \}</math> that have the properties | ||
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| + | (a) <math>f(A) \neq 0</math>, for <math>A \neq \phi</math>; | ||
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| + | (b) <math>f \left( A \cup B \right) = f \left( A \cap B \right) + f \left( A \Delta B \right)</math>, for all <math>A,B \in \mathcal P (M)</math>, where <math>A \Delta B = \left( A \cup B \right) \backslash \left( A \cap B \right)</math>. | ||
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==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
Revision as of 14:03, 7 May 2012
Problem
Let 
be a set composed of 
elements and let 
be its power set. Find all functions 
that have the properties
(a) 
, for 
;
(b) 
, for all 
, where 
.
Solution
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