Cho \(A=\left\{x\in R/\frac{1}{\left|x-2\right|}>2\right\}\);\(B=\left\{x\in R/\left|x-1\right|< 1\right\}\).Hãy tìm \(A\cup B,A\B\)
Xác định các tập: \(A\cup B,A\cap B;A\backslash B;B\backslash A\)
a, \(A=\left\{x\in R|-3\le x\le5\right\};B==\left\{x\in R|\left|x\right|< 4\right\}\)
b, \(A=\left[1;5\right];B=\left(-3;2\right)\cup\left(3;7\right)\)
c, \(A=\left\{x\in R|\dfrac{1}{\left|x-1\right|}\ge2\right\};B=\left\{x\in R|\left|x-2\right|\le1\right\}\)
d, \(A=\left[0;2\right]\cup\left(4;6\right);B=(-5;0]\cup\left(3;5\right)\)
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, \(A\cup B=(-5;2]\cup(3;6]\)
\(A\cap B=\left\{0\right\}\cup[4;5)\)
\(A\backslash B=(0;2]\cup\left[-5;6\right]\)
\(B\backslash A=[-5;0)\cup\left(3;4\right)\)
Cho \(A=\left\{x\in R|\left(x+1\right)^2+\left(x-1\right)^2=10\right\};B=\left\{x\in R|\left(x+1\right)^4+\left(x-1\right)^4=82\right\}\)Tìm tập X sao cho A\(\cup\)X=B.
Cho \(E=\left\{x\in Z|\left|x\right|\le5\right\}\); \(A=\left\{x\in R|x^2+3x-4=0\right\}\);
\(B=\left\{x\in Z|(x-2)(x+1)(2x^2-x-3)=0\right\}\)
a) CM \(A\subset E\),\(B\subset E\)
b) Tìm \(E\backslash\left(A\cap B\right)\),\(E\backslash\left(A\cup B\right)\) rồi tìm quan hệ giữa hai tập hợp này.
\(E=\left\{-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)
\(A=\left\{1;-4\right\}\)
\(B=\left\{2;-1\right\}\)
a) Với mọi x thuộc A đều thuộc E \(\Rightarrow A\subset E\)
Với mọi x thuộc B đều thuộc E \(\Rightarrow B\subset E\)
b) \(A\cap B=\varnothing\)
\(\Rightarrow E\backslash\left(A\cap B\right)=\left\{-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)
\(A\cup B=\left\{-4;-1;1;2\right\}\)
\(\Rightarrow E\backslash\left(A\cup B\right)=\left\{-5;-3;-2;0;3;4;5\right\}\)
\(\Rightarrow E\backslash\left(A\cup B\right)\subset E\backslash\left(A\cap B\right)\)
Cho tập \(A=\left(-\infty,-1\right)\cup\left(2,+\infty\right)\\ B=\left[-3.1\right]\)
Tìm m để \(C\dfrac{A}{B}\subset C\) biết \(C=\left\{x\in R\left|\left|2x-1\right|\le m\right|\right\}\)
1. \(A=\left\{x\in R\left|x-3\right|>4\right\}\)
\(B=\left\{x\in R\left|1-2x\right|< 2\right\}\)
\(A\cap B\) ; A\B; \(A\cup B\)
\(\left|x-3\right|>4\Rightarrow\left[{}\begin{matrix}x-3>4\\x-3< -4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>7\\x< -1\end{matrix}\right.\)
\(\Rightarrow A=\left(-\infty;-1\right)\cup\left(7;+\infty\right)\)
\(\left|2x-1\right|< 2\Leftrightarrow-2< 2x-1< 2\Leftrightarrow-\frac{1}{2}< x< \frac{3}{2}\)
\(\Rightarrow B=\left(-\frac{1}{2};\frac{3}{2}\right)\)
\(A\cap B=\varnothing\)
\(A\backslash B=A\)
\(A\cup B=\left(-\infty;-1\right)\cup\left(-\frac{1}{2};\frac{3}{2}\right)\cup\left(7;+\infty\right)\)
Cho A=\(\left\{x\in R,\left|x-2\right|\le3\right\}\), B=\(\left\{x\in R,\frac{x+3}{2-x}\le0\right\}\). Xác định \(A\cap B\) ; \(A\cup B\) ; A\B ; B\A
a, A = [ -2; 5)
B= ( - \(\infty\); 3 ]
C=(- \(\infty\) ; 4 )
Cho A = \(\left\{x\in R|1\le x\le5\right\}\), B = \(\left\{x\in R|4\le x\le7\right\}\), C = \(\left\{x\in R|2\le x\le6\right\}\)
a) Xác định \(A\cap B,A\cap C,B\cap C,A\cup C,\)A\\(\left(B\cup C\right)\)
b)Gọi D = \(\left\{x\in R|a\le x\le b\right\}\). Xác định a, b để \(D\subset A\cap B\cap C\)
Tìm phần bù của các tập hợp sau theo R:
a, \(A=[-12;10)\)
b, \(B=\left(-\infty;-2\right)\cup\left(2;+\infty\right)\)
c, \(C=[3;+\infty)\backslash\left\{5\right\}\)
d, \(D=\left\{x\in R|-4< x+2\le5\right\}\)