Question

Bună ziua, am o mare rugăminte sa ma ajutați, va rog frumos

Answer 1

4)

$\it A=(0,\ \infty);\ \ \ B=[-2,\ 2]\\ \\ A\cap B=[-2,\ \infty)\\ \\ A\cup B=(0,\ 2]\\ \\ A\setminus B=(2,\ \infty)\\ \\ A\cap \mathbb{N}=\mathbb{N}^*\\ \\ B\cap\mathbb{N}=\{0,\ 1,\ 2\}\\ \\ B\cap\mathbb{Z}=\{-2,\ -1,\ 0,\ 1,\ 2\}$

5)

$\it a)\ \dfrac{1}{4}\not\in\Big(-\dfrac{1}{3},\ \dfrac{2}{5} \Big )\ \ \ (F),\ deoarece\ \dfrac{1}{4}<\dfrac{2}{5} \\ \\ b)\ 6\in(-2,\ 6]\ \ \ (A),\ deoarece\ intervalul\ e\ \^{i}nchis\ la\ dreapta$

$\it c)\ \ 7\not\in\Big[\dfrac{62}{9},\ \dfrac{64}{9} \Big ]\ \ \ (F),\ deoarece\ 7=\dfrac{63}{9}<\dfrac{64}{9} \\ \\ \\ d)\ \ \dfrac{\sqrt2}{2}\in(-\infty,\ 0) \ \ \ \ (F),\ deoarece\ \dfrac{\sqrt2}{2}>0$

6)

$\it a)\ \ x\in\Big[-\dfrac{4}{3},\ \dfrac{2}{7} \Big] \Leftrightarrow -\dfrac{4}{3}\leq x\leq\dfrac{2}{7} \\ \\ \\ b)\ x\not\in(3,\ \infty) \Leftrightarrow x\leq3\\ \\ c)\ x\in(-\sqrt2,\ \infty) \Leftrightarrow -\sqrt2<x<\infty\\ \\ e)\ -3\leq4x-1\leq5|_{+1}\Leftrightarrow -2\leq 4x\leq6|_{:4} \Leftrightarrow -\dfrac{1}{2}\leq x\leq\dfrac{3}{2}\Leftrightarrow A=[-\dfrac{1}{2},\ \dfrac{3}{2} ]$