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a, \(A\cup B=(-4;5]\)
\(A\cap B=[-3;4)\)
\(A\backslash B=\left[4;5\right]\)
\(B\backslash A=\left(-4;-3\right)\)
b, \(A\cup B=\left(-3;7\right)\)
\(A\cap B=[1;2)\cup(3;5]\)
\(A\backslash B=\left[2;3\right]\)
\(B\backslash A=\left(-3;1\right)\cup\left(5;7\right)\)
c, \(A\cup B=\left[\dfrac{1}{2};3\right]\)
\(A\cap B=\left[1;\dfrac{3}{2}\right]\)
\(A\backslash B=[\dfrac{1}{2};1)\)
\(B\backslash A=(\dfrac{3}{2};3]\)
d, \(A\cup B=(-5;2]\cup(3;6]\)
\(A\cap B=\left\{0\right\}\cup[4;5)\)
\(A\backslash B=(0;2]\cup\left[-5;6\right]\)
\(B\backslash A=[-5;0)\cup\left(3;4\right)\)
\(\frac{1}{\left|x-2\right|}>2\Rightarrow\left|x-2\right|< \frac{1}{2}\Rightarrow-\frac{1}{2}< x-2< \frac{1}{2}\)
\(\Rightarrow\frac{3}{2}< x< \frac{5}{2}\)
\(\Rightarrow A=\left(\frac{3}{2};\frac{5}{2}\right)\)
\(\left|x-1\right|< 1\Rightarrow-1< x-1< 1\Rightarrow0< x< 2\)
\(\Rightarrow B=\left(0;2\right)\)
\(\Rightarrow A\cup B=\left(0;\frac{5}{2}\right)\)
\(A\backslash B=[2;\frac{5}{2})\)
\(A=\left\{-2;-1;0;1;2\right\}\)
\(C=\left\{-2;\frac{3}{2};2\right\}\)
\(\Rightarrow B\cup C=\left\{-2;0;1;\frac{3}{2};2;3\right\}\)
\(\Rightarrow A\cap\left(B\cup C\right)=\left\{-2;0;1;2\right\}\)
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a: A=(-7/4; -1/2]
\(B=\left(-\dfrac{9}{2};-4\right)\cup\left(4;\dfrac{9}{2}\right)\)
\(C=\left(\dfrac{2}{3};+\infty\right)\)
b: \(\left(A\cap B\right)\cap C=\varnothing\)
\(\left(A\cup C\right)\cap\left(B\A\right)\)
\(=(-\dfrac{7}{4};-\dfrac{1}{2}]\cup\left(\dfrac{2}{3};+\infty\right)\cap\left[\left(-\dfrac{9}{2};-4\right)\cup\left(4;\dfrac{9}{2}\right)\right]\)
\(=\left(4;\dfrac{9}{2}\right)\)
B= -2≤x ≤ 2 A= 0 <x< 2 A ∪ B = B A ∩ B = A ⇒ đáp án : -2 ≤ x ≤ 0 và x=2