Question

Una ziua! Ma puteți ajuta?

Answer 1

Explicație pas cu pas:

$A = \Big\{-3,74; -1,(7); \sqrt {1}; \sqrt{2}; \dfrac{ \sqrt{ {4}^{2} } }{2}; \sqrt{1 \dfrac{7}{9} } \Big\}$

$-3,74 \in \mathbb{Q}$

$-1,(7) \in \mathbb{Q}$

$\sqrt {1} = 1 \in \mathbb{N}$

$\sqrt{2} \in \mathbb{R - Q}$

$\dfrac{ \sqrt{ {4}^{2} } }{2} = \dfrac{4}{2} = 2 \in \mathbb{N}$

$\sqrt{1 \dfrac{7}{9} } = \sqrt{ \dfrac{16}{9} } = \dfrac{4}{3} \in \mathbb{Q}$

=>

$A \cap \mathbb{N} = \Big\{\sqrt {1}; \dfrac{ \sqrt{ {4}^{2} } }{2}\Big\}$

$A \cap \mathbb{Z} = \Big\{\sqrt {1}; \dfrac{ \sqrt{ {4}^{2} } }{2}\Big\}$

$A \cap \mathbb{Q} = \Big\{-3,74; -1,(7); \sqrt {1}; \dfrac{ \sqrt{ {4}^{2} } }{2}; \sqrt{1 \dfrac{7}{9} } \Big\}$

$A \cap (\mathbb{R - Q}) = \Big\{\sqrt{2}\Big\}$