Question

Fie multimile A = {-6;3;6} si B = {-2;-1:2} . Determinati elementele multimii C = {x=a/b l a apartine A si x apartine lui B

Answer 1

$A = \Big\{-6;3;6\Big\} \quad si \quad B = \Big\{-2;-1;2\Big\} \\ \\ C = \Big\{x= \dfrac{a}{b}\Big| a\in A si b\in B\Big\} \\ \\ Luam toate cazurile posibile: \\ \\ x \in\Big\{\dfrac{-6}{-2}; \dfrac{-6}{-1};\dfrac{-6}{2};\dfrac{3}{-2};\dfrac{3}{-1};\dfrac{3}{2};\dfrac{6}{-2};\dfrac{6}{-1};\dfrac{6}{2}\Big\} \Rightarrow \\ \\ \Rightarrow x\in \Big\{3;6;-3;-\dfrac{3}{2};-3;\dfrac{3}{2};-3;-6;3\Big\} \Rightarrow$

$\Rightarrow x\in \Big\{-6;-3;-\dfrac{3}{2};\dfrac{3}{2};3;6\Big\} \Rightarrow \boxed{C =\Big\{-6;-3;-\dfrac{3}{2};\dfrac{3}{2};3;6\Big\}}$