Đáp án:
$A=\{x\in \mathbb{R} / |2x-1|<2\}
=\left ( -\dfrac{1}{2};\dfrac{3}{2} \right )\\
B=\{x\in \mathbb{R}/ |x-1|>4\}=(-3;5)\\
C=(0;6)\\
a)
A\cup B=(-3;5)\\
A\cap B=\left ( \dfrac{-1}{2};\dfrac{3}{2} \right )\\
C_RA=\left (-\infty;-\dfrac{1}{2} \right ]\cup \left [\dfrac{3}{2};+\infty \right )\\
A\setminus B=\varnothing \\$
Giải thích các bước giải:
$A=\{x\in \mathbb{R} / |2x-1|<2\}
=\left ( -\dfrac{1}{2};\dfrac{3}{2} \right )\\
B=\{x\in \mathbb{R}/ |x-1|>4\}=(-3;5)\\
C=(0;6)\\
a)
A\cup B=(-3;5)\\
A\cap B=\left ( \dfrac{-1}{2};\dfrac{3}{2} \right )\\
C_RA=R\setminus A=\left (-\infty;-\dfrac{1}{2} \right ]\cup \left [\dfrac{3}{2};+\infty \right )\\
A\setminus B=\varnothing \\
b)
B\setminus C=(-3;0]\\
A\cap (B\setminus C)=\left ( \dfrac{-1}{2};0 \right ]\\
(A\cap B)\setminus C=\left ( \dfrac{-1}{2};0 \right ]\\
\Rightarrow A\cap (B\setminus C)=(A\cap B)\setminus C (đpcm)$
