Question

Va roggg!
Ex 4!​Mulțumesc!

Answer 1

$A = \Big\{x\in \mathbb{Z}\,\Big|\,\big|x|\leq 3\Big\}\,\text{ si }\,B = \Big\{x\in \mathbb{Z}^*\,\Big|\,\big|x|= -x\Big\}\\ \\ \\A:\\ \\|x|\leq 3\,\,\Leftrightarrow\,\,-3\leq x\leq 3\,\,\Rightarrow\,\, A = \{-3,-2,-1,0,1,2,3\}$

$\\B:\\ \\ |x| = -x\\\\\boxed{1}\quad x<0\,\,\Rightarrow -x = -x \,\,(A)\,\, \Rightarrow\,\, x<0 \,\, \Rightarrow B = \{...,-4,-3,-2,-1\} \\ \boxed{2}\quad x> 0\,\, \Rightarrow +x = -x\,\, \Rightarrow\,\,-2x = 0 \Rightarrow\,\, x = 0\,\,(F) \\ \\ \text{Din }\boxed{1}\,\cup\,\boxed{2}\,\,\Rightarrow B =\{...,-4,-3,-2,-1\}$

$\\\Rightarrow\,\,A\cap B = \{-3,-2,-1,0,1,2,3\} \cap \{....,-4,-3,-2,-1\}\\ \\\Rightarrow\,\,\boxed{A\cap B = \{-3,-2,-1\}}$