Question

Va rog mult, sa ma ajutati la exercitiul urmator: determinati cardinalul multimii B={x apartine Z | 10< |x| < 40}. Multumesc

Answer 1

B={x ∈ Z | 10< |x| < 40}. 

|x| = x

10< x < 40

x₁ ∈{ 11; 12; 13;  .... 39}. 

x₂∈{ -39; -38; .... -11.}

Obs. 11 ...  20 = 10 nr.                     -39 ... -30 =  10nr

         21 .... 30 = 10 nr.                    -29 ... - 20 = 10 nr.

         31 .... 39 =   9 nr.                    -19 ... - 11 =   9 nr
______________________           ________________
        
        11 .... 39  = 29 nr.                    - 39 .... -11 = 29 nr

Card. B = 58 elem.

Answer 2

   
[tex]\displaystyle\\ B = \{x \in Z~ \Big| ~10\ \textless \ |x| \ \textless \ 40\}\\\\ 10\ \textless \ |x|\ \textless \ 40 ~~\Longleftrightarrow~~ \begin{cases} 10\ \textless \ x\ \textless \ 40 ~~~~~~~daca ~~x\ \textgreater \ 0\\ -40\ \textless \ x\ \textless \ -10~~~daca ~~x\ \textless \ 0 \end{cases} \\\\ B=\{-39;~-38;~-37;~-36;~\cdots~;~-11\}\bigcup \{11;~12;~13;~\cdots~;~39 \}\\\\ n = 2(39-11 + 1) =2(28+1)=2\times 29 = 58 \text{ de elemente are B}\\\\ \Longrightarrow~~~ \text{card A}=58[/tex]