Question

1) fie multimile A={×€|N /2×+2€ D12} ; B={×€|N /5 ≤3×-1≤11}. Determinati multimile A,B, A -B, A Π B, B-A, A U B.

Answer 1

     
[tex]A=\{x\in N | 2x+2 \in D_{12}\} \\ D_{12}=\{1;~2;~3;~4;~6;~12\} \\ 2x+2=1~~~~~~~\Longrightarrow ~~~x= \frac{-1}{2}\notin N \\ 2x+2=2~~~~~~~\Longrightarrow ~~~x= 0 \in N \\ 2x+2=3~~~~~~~\Longrightarrow ~~~x= \frac{1}{2}\notin N \\ 2x+2=4~~~~~~~\Longrightarrow ~~~x= 1 \in N \\ 2x+2=6~~~~~~~\Longrightarrow ~~~x= 2 \in N \\ 2x+2=12~~~~~\,\Longrightarrow ~~~x= 5 \in N \\ \Longrightarrow ~~~\boxed{A=\{0;~1;~2;~5\}} [/tex]


[tex]5 \leq 3x-1 \leq 11 \\ 5\leq 3x-1 \\ 5+1 \leq 3x \\ x \geq \frac{6}{3} \\ x \geq 2 \\ ----- \\ 3x-1 \leq 11 \\ 3x \leq 11+1 \\ x \leq \frac{12}{3} \\ x \leq 4 \\ ----- \\\boxed{B=\{2;~3;~4\}}[/tex]


[tex]A=\{0;~1;~2;~5\} \\ B=\{2;~3;~4\} \\ A-B=\{0;~1;~5\} \\ A \bigcap B = \{2\} \\ B-A=\{3;~4\} \\ A \bigcup B = \{0;~1;~2;~3;~4;~5\}[/tex]