共50条信息
设集合\(A=\left\{ \left.x \right|0.{4}^{x} < 1\right\} \),集合\(B=\left\{ \left.x \right|y=\lg \left({x}^{2}-x-2\right)\right\} \),则集合\(A∪\left({C}_{R}B\right)= (\) \()\)
已知集合\(A=\{x|{{x}^{2}}-3x-4 > 0\},B=(x\in N|x\leqslant 2\}\),则\((∁_{R}A)∩B=(\) \()\)
已知全集\(U=R\),集合\(A=\{x||x-1| < 1\}\),\(B=\{x|\dfrac{2x-5}{x-1}\geqslant 1\}\),则\(A\cap {{C}_{U}}B=\)( )
已知集合\(U=R\),集合\(A=\{x|x < 2\}\),\(B=\{x|\lg (x-1) > 0\}\),则\(A\cap \left( {{C}_{U}}B \right)=(\) \()\)
设集合\(A\)\(=\{\)\(x\)\(|-1\leqslant \)\(x\)\(\leqslant 2\}\),\(B\)\(=\{\)\(x\)\(|\)\(x\)\({\,\!}^{2}-(2\)\(m\)\(+1)\)\(x\)\(+2\)\(m\)\( < 0\}\).
\((1)\)当\(m\)\( < \dfrac{1}{2}\)时,化简集合\(B\);
\((2)\)若\(A\)\(∪\)\(B\)\(=\)\(A\),求实数\(m\)的取值范围.
已知集合\(A=\{x|{{x}^{2}}-4x+3=0\},B=\{x|{{x}^{2}}-ax+9=0\},\)若\(B\bigcap \left( {{\complement }_{R}}A \right)=\varnothing ,\) 试求实数\(a\)的范围.
\(.\) 已知函数\(f(x)= \sqrt{x-3}- \dfrac{1}{ \sqrt{7-x}} \)的定义域为集合\(A\),\(B=\{x∈Z|2 < x < 10\}\),\(C=\{x∈R|x < a\)或\(x > a+1\}\)
\((1)\)求\(A\), \((∁_{R}A)∩B\);
\((2)\)若\(A∪C=R\),求实数\(a\)的取值范围.
设集合\(A=\left\{ (x,y)\left| {{(x-3)}^{2}}+{{(y-4)}^{2}}=\dfrac{4}{5} \right. \right\}\),\(B=\left\{ (x,y)\left| {{(x-3)}^{2}}+{{(y-4)}^{2}}=\dfrac{36}{5} \right. \right\}\),\(C=\left\{ (x,y)\left| 2\left| x-3 \right|+\left| y-4 \right|=\lambda \right. \right\}\),若\((A\bigcup B)\bigcap C\ne \varnothing \),则实数\(\lambda \)的取值范围是( )
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