Dùng các kí hiệu đoạn, khoảng, nửa khoảng để viết các tập hợp sau đ

$$\begin{gathered} a) \left\{x \in \mathrm{ℝ}\overline{) -2<x}<3\right\}; \\ b) \left\{x \in \mathrm{ℝ}\overline{) 1\le x\le 10}\right\}; \\ c) \left\{x \in \mathrm{ℝ}\overline{) -5<x\le \sqrt{3}}\right\}; \\ d) \left\{x \in \mathrm{ℝ}\overline{) \mathrm{\pi }\le x<4}\right\}; \\ e) \left\{x \in \mathrm{ℝ}\overline{) x<\frac{1}{4}}\right\}; \\ g) \left\{x \in \mathrm{ℝ}\overline{) x\ge \frac{\mathrm{\pi }}{2}}\right\}. \end{gathered}$$

Hướng dẫn giải

$$\begin{gathered} a) \left\{x \in \mathrm{ℝ}\overline{) -2<x}<3\right\} = \left(-2;3\right) \\ b) \left\{x \in \mathrm{ℝ}\overline{) 1\le x\le 10}\right\} = \left[1;10\right] \\ c) \left\{x \in \mathrm{ℝ}\overline{) -5<x\le \sqrt{3}}\right\} = (-5;\sqrt{3}\left] \\ d\right) \left\{x \in \mathrm{ℝ}\overline{) \mathrm{\pi }\le x<4}\right\} =[\mathrm{\pi };4) \\ e) \left\{x \in \mathrm{ℝ}\overline{) x<\frac{1}{4}}\right\} = (-\infty ;\frac{1}{4}\left) \\ g\right) \left\{x \in \mathrm{ℝ}\overline{) x\ge \frac{\mathrm{\pi }}{2}}\right\} = [\frac{\mathrm{\pi }}{2};+\infty ) \end{gathered}$$