n multimi

[alex2008]

Fie \( A_1 , A_2 , ..., A_n \) , n multimi \( (n\ge2) \) . Dovediti ca pentru oricare doua numere naturale \( i,j (1\le i\le n)(1\le j\le n) \) , avem :
\( (A_1\cap A_2\cap\ ...\ \cap A_i)\cap(A_{i+1}\cap\ ...\ \cap A_n)=(A_1\cap A_2\cap\ ...\ \cap A_j)\cap(A_{j+1}\cap\ ...\ \cap A_n) \)
si \( (A_1\cup A_2\cup\ ...\ \cup A_i)\cup(A_{i+1}\cup\ ...\ \cup A_n)=(A_1\cup A_2\cup\ ...\ \cup A_j)\cup(A_{j+1}\cup \ ...\ \cup A_n) \)
De asemenea , daca\( i_1,i_2,...,i_n \) sunt numerele \( 1,2,...,n \) , scrise intr-o alta ordine , atunci\( A_1\cup A_2\cup\ ...\ \cup A_n=A_{i_1}\cup A_{i_2}\cup\ ...\ \cup A_{i_n} \)
si \( A_1\cap A_2\cap\ ...\ \cap A_n=A_{i_1}\cap A_{i_2}\cap\ ...\ \cap A_{i_n} \)