Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

m (→‎Problem)
m (→‎See also)
Line 9: Line 9:
 
{{solution}}
 
{{solution}}
  
−
==See also==
+
==See Also==
 
*[[2006 Romanian NMO Problems/Grade 9/Problem 1 | Previous problem]]
 
*[[2006 Romanian NMO Problems/Grade 9/Problem 1 | Previous problem]]
 
*[[2006 Romanian NMO Problems/Grade 9/Problem 3 | Next problem]]
 
*[[2006 Romanian NMO Problems/Grade 9/Problem 3 | Next problem]]
 
*[[2006 Romanian NMO Problems]]
 
*[[2006 Romanian NMO Problems]]
 
[[Category:Olympiad Geometry Problems]]
 
[[Category:Olympiad Geometry Problems]]

Revision as of 14:03, 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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_Romanian_NMO_Problems/Grade_10/Problem_1&oldid=46887"