O problema cu multimi
Posted: Fri Feb 27, 2009 1:28 pm
Fie \( n\geq 2 \) un numar intreg, multimea \( A=\{1,2,\dots,n\} \) si \( n \) submultimi distincte \( A_{1},A_{2},\dots,A_{n} \) ale multimii \( A \).
Demonstrati ca exista \( x\in A \) astfel incat multimile \( A_{1}\backslash \{x\}, A_{2}\backslash\{x\},\dots, A_{n}\backslash\{x\} \) sa fie distincte.
Demonstrati ca exista \( x\in A \) astfel incat multimile \( A_{1}\backslash \{x\}, A_{2}\backslash\{x\},\dots, A_{n}\backslash\{x\} \) sa fie distincte.