优优班--学霸训练营 > 知识点挑题
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            • 1.
              若\(A=\{1,4, \)\(x\)\(\}\),\(B=\{1, \)\(x\)\({\,\!}^{2}\}\),且\(A∩B=B\),则 \(x\)的取值集合是\((\)  \()\)
              A.\(\left\{-1,0,2\right\} \)  
              B.\(\left\{0,1,-2,2\right\} \)  
              C.\(\left\{-1,1,2\right\} \)  
              D.\(\left\{0,-2,2\right\} \)
            • 2.

              已知集合\(A=\{x\{-3\leqslant x\leqslant 5),B=\{x|m+1 < x < 2m-1)\),\(C=\{x∈Z|x∈A\)或\(x∈B)\).

              \((1)\)当\(m=3\)时,用列举法表示集合\(C\);

              \((2)\)若\(A∩B=B\),求实数\(m\)的取值范围.

            • 3.

              已知集合\(A=\left\{ x\left| {{x}^{2}}-3x+2\geqslant 0 \right. \right\},B=\left\{ x\left| x\geqslant t \right. \right\}\),若\(A∪B=A \),则实数\(t\)的取值范围为_________\(.\) 

            • 4.

              若集合\(A{=}\{ 0{,}m\}{,}B{=}\{ 1{,}2\}{,}A{∩}B{=}\{ 1\}\),则实数\(m{=}\)______.

            • 5.

              集合\(A=\left\{x \left|x < a \right.\right\} \),\(B=\left\{x \left|1 < x < 2 \right.\right\} \),若\(A∪{C}_{R}B=R \),则实数\(a\)的取值范围是

              A.\(a\leqslant 1\)
              B.\(a < 1\)
              C.\(a\geqslant 2\)
              D.\(a > 2\) 
            • 6.

              已知集合 \(P=\left\{ x\left| {{x}^{2}}\leqslant 1 \right. \right\}\) ,\(M=\left\{ a \right\}.\)若\(P\bigcup M=P\),则\(a\)的取值范围是(    )

              A.\(\left( -\infty ,\left. -1 \right] \right.\)
              B.\(\left[ 1,+\infty \right)\)
              C.\(\left[ -1,1 \right]\)
              D.\(\left( -\infty ,-1 \right]\bigcup \left[ 1,+\infty \right)\) 
            • 7.

              若\(A=\{a\}\),\(B=\{0,a^{2}\}\),\(A⊆B\),则实数\(a=\)_______.

            • 8.

              已知\(p: \dfrac{x+4}{x} > 2 \),\(q:x^{2}-4x+4-m^{2} < 0 (m > 0)\),命题“若\(¬ p\)则\(¬ q\)”为假命题,命题“若\(¬ q\)则\(¬ p\)”为真命题,求实数\(m\)的取值范围.

            • 9.

              已知集合\(A=\{x|{x}^{2}+3x-4\leqslant 0\} \),\(B=\{x|2-a\leqslant x\leqslant 2+a,a > 0\} \).

              \((1)\)若\(A⊆B \),求\(a\)的取值范围;

              \((2)\)若\(A∩B=\varnothing \),求\(a\)的取值范围.

            • 10. 已知集合\(A=\{-1,0,2\}\),\(B=\{2^{a}\}\),若\(B⊆A\),则实数\(a\)的值为 ______ .
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