Question

Cho \(A=\left\{x\in R/\frac{1}{\left|x-2\right|}>2\right\}\);\(B=\left\{x\in R/\left|x-1\right|< 1\right\}\).Hãy tìm \(A\cup B,A\B\)

Answer 1

\(\frac{1}{\left|x-2\right|}>2\Rightarrow\left|x-2\right|< \frac{1}{2}\Rightarrow-\frac{1}{2}< x-2< \frac{1}{2}\)

\(\Rightarrow\frac{3}{2}< x< \frac{5}{2}\)

\(\Rightarrow A=\left(\frac{3}{2};\frac{5}{2}\right)\)

\(\left|x-1\right|< 1\Rightarrow-1< x-1< 1\Rightarrow0< x< 2\)

\(\Rightarrow B=\left(0;2\right)\)

\(\Rightarrow A\cup B=\left(0;\frac{5}{2}\right)\)

\(A\backslash B=[2;\frac{5}{2})\)