Question

Rezolva ex din imagine

Answer 1

$A = \Big\{- 1; 7; 0; \dfrac{8}{4}; 23; \dfrac{1}{9}; \dfrac{8}{11}; 5,8; -\dfrac{7}{19}; 9,(78); 89,(7); -4; -\dfrac{65}{5}\Big\}$

$- 1 \in \mathbb{Z} \ ; \ 7 \in \mathbb{N} \ ; \ 0 \in \mathbb{N} \ ; \ \dfrac{8}{4} = 2 \in \mathbb{N} \ ; \ 23 \in \mathbb{N}$

$\dfrac{1}{9} \in \mathbb{Q} \ \ ; \ \ \dfrac{8}{11} \in \mathbb{Q} \ \ ; \ \ 5,8 \in \mathbb{Q} \ \ ; \ \ -\dfrac{7}{19} \in \mathbb{Q}$

$9,(78) = \dfrac{978-9}{99} = \dfrac{323}{33} \in \mathbb{Q}$

$89,(7) = \dfrac{897-89}{9} = \dfrac{808}{9} \in \mathbb{Q}$

$-4 \in \mathbb{Z} \ ; \ \ -\dfrac{65}{5} = - 13 \in \mathbb{Z}$

$A \cap \mathbb{N} = \Big\{7; 0; \dfrac{8}{4}; 23\Big\}$

$A \cap \mathbb{Z} = \Big\{- 1; 7; 0; \dfrac{8}{4}; 23; -4; -\dfrac{65}{5}\Big\}$

$A \cap \mathbb{Q} = \Big\{- 1; 7; 0; \dfrac{8}{4}; 23; \dfrac{1}{9}; \dfrac{8}{11}; 5,8; -\dfrac{7}{19}; 9,(78); 89,(7); -4; -\dfrac{65}{5}\Big\}$

$\iff A \cap \mathbb{Q} = A$

$A \cap (\mathbb{Z} - \mathbb{N} ) = \Big\{- 1; -4; -\dfrac{65}{5}\Big\}$