\(P\cap Q=\varnothing\Leftrightarrow\left[{}\begin{matrix}a+1< -5\\a-1>4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a< -6\\a>5\end{matrix}\right.\)
\(\Rightarrow P\cap Q\ne\varnothing\Leftrightarrow-6\le a\le5\)
Vậy: \(a\in\left[-6;5\right]\).
Bài 18 :
\(\left(-\infty;9a\right)\cap\left(\dfrac{4}{a};+\infty\right)\ne\varnothing\) \(\left(a< 0\right)\)
\(\Rightarrow9a>\dfrac{4}{a}\)
\(\Leftrightarrow9a-\dfrac{4}{a}>0\)
\(\Leftrightarrow\dfrac{9a^2-4}{a}>0\)
\(\Leftrightarrow9a^2-4< 0\left(a< 0\right)\)
\(\Leftrightarrow9a^2< 4\)
\(\Leftrightarrow a^2< \dfrac{4}{9}=\left(\dfrac{2}{3}\right)^2\)
\(\Leftrightarrow-\dfrac{2}{3}< a< \dfrac{2}{3}\)
mà \(a< 0\)
\(\Leftrightarrow-\dfrac{2}{3}< a< 0\)
Bài 16 :
\(\left\{{}\begin{matrix}A=(-3;5]\\B=[0;+\infty)\end{matrix}\right.\)
\(A\cap B=\left\{0;1;2;3;4;5\right\}\)
\(A\) \\(B=\left\{-2;-1\right\}\)
\(C_RB=\left(-\infty;0\right)\)
\(A\cap N=\left\{0;1;2;3;4;5\right\}\)
Bài 15 :
\(A=\left\{x\in R|x\ge3\right\}\)
\(\Rightarrow A=[3;+\infty)\)
\(B=\left\{x\in R|-1< x\le9\right\}\)
\(\Rightarrow B=(-1;9]\)
\(C=\left\{x\in R|\left|x-1\right|\le3\right\}\)
\(\left|x-1\right|\le3\Leftrightarrow-3\le x-1\le3\Leftrightarrow-2\le x\le4\)
\(\Rightarrow C=\left[-2;4\right]\)
\(A\cap B=\left[3;9\right]\)
\(A\)\\(B=\left(9;+\infty\right)\)
\(C_RB=(-\infty;1]\cup\left(9;+\infty\right)\)
Ta có :
\(B\cap C=(-1;4]\)
\(\Rightarrow A\cup\left(B\cap C\right)=\left(-1;+\infty\right)\)
