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Bài 3:
a: \(\left(-\infty;\dfrac{1}{3}\right)\cap\left(\dfrac{1}{4};+\infty\right)=\left(\dfrac{1}{4};\dfrac{1}{3}\right)\)
b: \(\left(-\dfrac{11}{2};7\right)\cup\left(-2;\dfrac{27}{2}\right)=\left(-\dfrac{11}{2};\dfrac{27}{2}\right)\)
c: \(\left(0;12\right)\text{\[}5;+\infty)=\left(0;5\right)\)
d: \(R\[ -1;1)=\left(-\infty;-1\right)\cup[1;+\infty)\)
có 2x-1<5 =>A=(-\(\infty\);3)
A\(\cup\)B=(-\(\infty\);3)
A\(\cap\)B=(-\(\infty\);2]
A/B=(2;3)
a: \(\left(A\cap B\right)\cap C=(4;10]\cap\left(5;+\infty\right)=(5;10]\)
c: A\B=[3;4]
B\C=(4;5]
C\A=[3;5]
d: (A\B) giao C=[3;4] giao (5;+\(\infty\))=[4;5)
a/ A = (3;\(+\infty\)), B=[0;4]
A \(\cap\) B= (3;4)
A\(\cup\) B=[0;+\(\infty\))
A\B= (4;\(+\infty\))
B\A= [0;3]
b/ A=(\(-\infty\);4], B=(2;\(+\infty\))
A\(\cap\)B=(2;4]
A\(\cup\)B= R
A\B= (\(-\infty\);2]
B\A=(4;\(+\infty\))
c/ A=[0;4] , B=(\(-\infty\);2]
A\(\cap\)B= [0;2)
\(A\cup B\) = (\(-\infty\);4]
A\ B=[2;4]
B\A=(\(-\infty\);0)
Để A có nghĩa \(\Rightarrow\frac{m+1}{2}\ge m-1\Rightarrow m\le3\)
a/ \(A\subset B\Leftrightarrow\left[{}\begin{matrix}\frac{m+1}{2}< -2\\m-1\ge2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m< -5\\m\ge3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m< -5\\m=3\end{matrix}\right.\)
b/ \(A\cap B=\varnothing\Leftrightarrow\left\{{}\begin{matrix}m-1\ge-2\\\frac{m+1}{2}< 2\end{matrix}\right.\)
\(\Leftrightarrow-1\le m< 3\)
Lời giải:
Ta có:
\(A\cap B=\left\{x\in\mathbb{R}|1< x< 2\right\}\)
\(A\cup B=\left\{x\in\mathbb{R}|x> -1\right\}\)
B\A=(-2;0)
A\B=\(\emptyset\)
A\(\cup\)B=(-2;+\(\infty\) )
A\(\cap\)B=[0;7]