對口單招集合題庫及答案

一、單項選擇題(每題2分,共10題)1.已知集合\(A=\{1,2,3\}\),集合\(B=\{2,3,4\}\),則\(A\capB\)為（）A.\(\{1\}\)B.\(\{2,3\}\)C.\(\{4\}\)D.\(\{1,2,3,4\}\)答案：B2.設全集\(U=\{1,2,3,4,5\}\),集合\(A=\{1,3,5\}\),則\(\complement_{U}A\)為()A.\(\{2,4\}\)B.\(\{1,2,3,4,5\}\)C.\(\varnothing\)D.\(\{1,3,5\}\)答案：A3.若集合\(A=\{x|x\gt1\}\),集合\(B=\{x|x\lt3\}\),則\(A\capB\)為()A.\(\{x|1\ltx\lt3\}\)B.\(\{x|x\gt1\}\)C.\(\{x|x\lt3\}\)D.\(\varnothing\)答案：A4.已知集合\(A=\{a,b,c\}\),集合\(B=\{d\}\),則\(A\cupB\)的元素個數(shù)為()A.\(3\)B.\(4\)C.\(5\)D.\(6\)答案：B5.若集合\(A=\{x|x^{2}-1=0\}\),則\(A\)的元素為()A.\(\{1\}\)B.\(\{-1\}\)C.\(\{1,-1\}\)D.\(\varnothing\)答案：C6.設集合\(A=\{x|x\)是奇數(shù)\(\}\),集合\(B=\{x|x\)是整數(shù)\(\}\),則\(A\)與\(B\)的關(guān)系是()A.\(A=B\)B.\(A\subseteqB\)C.\(B\subseteqA\)D.\(A\capB=\varnothing\)答案：B7.已知集合\(A=\{1,2\}\),集合\(B=\{1,2,3,4\}\),則滿足\(A\subseteqC\subseteqB\)的集合\(C\)有()個A.\(2\)B.\(3\)C.\(4\)D.\(5\)答案：C8.若集合\(A=\{x|x^{2}+2x-3=0\}\),集合\(B=\{-3,1\}\),則\(A\)與\(B\)的關(guān)系是()A.\(A\neqB\)B.\(A=B\)C.\(A\subsetneqqB\)D.\(B\subsetneqqA\)答案：B9.設全集\(U=\{1,2,3,4,5,6\}\),集合\(A=\{1,3,5\}\),集合\(B=\{2,4,6\}\),則\((\complement_{U}A)\cap(\complement_{U}B)\)為()A.\(\varnothing\)B.\(U\)C.\(\{1,2,3,4,5,6\}\)D.\(\{1,2,3,4,5,6\}\)答案：A10.若集合\(A=\{x|x\geq0\}\),集合\(B=\{x|x\lt2\}\),則\(A\cupB\)為()A.\(\{x|0\leqx\lt2\}\)B.\(\{x|x\geq0\}\)C.\(\{x|x\lt2\}\)D.\(R\)答案：D二、多項選擇題(每題2分,共10題)1.下列說法正確的是(）A.空集是任何集合的子集B.任何集合至少有兩個子集C.若\(A\subseteqB\),\(B\subseteqC\),則\(A\subseteqC\)D.若\(A\capB=A\),則\(A\subseteqB\)答案:ACD2.已知集合\(A=\{1,2\}\),集合\(B\)滿足\(A\cupB=\{1,2,3\}\),則集合\(B\)可以是()A.\(\{3\}\)B.\(\{1,3\}\)C.\(\{2,3\}\)D.\(\{1,2,3\}\)答案:ABCD3.若集合\(A=\{x|x^{2}-4x+3=0\}\),集合\(B=\{x|x^{2}-1=0\}\),則\(A\capB\)為()A.\(\{1\}\)B.\(\{-1\}\)C.\(\{3\}\)D.\(\varnothing\)答案：A4.設全集\(U=\{1,2,3,4,5\}\),集合\(A=\{1,2\}\),則\(\complement_{U}A\)的子集有()A.\(\varnothing\)B.\(\{3\}\)C.\(\{3,4\}\)D.\(\{1,2,3,4,5\}\)答案:ABC5.若集合\(A=\{x|x\)是三角形\(\}\),集合\(B=\{x|x\)是等腰三角形\(\}\),集合\(C=\{x|x\)是等邊三角形\(\}\),則()A.\(C\subseteqB\)B.\(B\subseteqA\)C.\(A\subseteqC\)D.\(C\subseteqA\)答案:ABD6.已知集合\(A=\{1,2,3\}\),集合\(B=\{2,3,4\}\),則\(A\capB\)與\(A\cupB\)分別為()A.\(\{2,3\}\)B.\(\{1,2,3\}\)C.\(\{2,3,4\}\)D.\(\{1,2,3,4\}\)答案:AD7.若集合\(A=\{x|x\gt-1\}\),集合\(B=\{x|x\lt3\}\),則()A.\(A\capB=\{x|-1\ltx\lt3\}\)B.\(A\cupB=R\)C.\(A\subseteqB\)D.\(B\subseteqA\)答案：A8.設集合\(A=\{1\}\),集合\(B=\{1,2,3\}\),下列說法正確的是()A.\(A\subseteqB\)B.\(A\inB\)C.\(\{A\}\subseteqB\)D.\(\{1\}\inB\)答案：A9.若集合\(A=\{x|x^{2}=x\}\),集合\(B=\{0,1\}\),則()A.\(A=B\)B.\(A\subseteqB\)C.\(B\subseteqA\)D.\(A\capB=A\)答案:ABD10.已知全集\(U=\{1,2,3,4,5\}\),集合\(A=\{1,2\}\),集合\(B=\{2,3,4\}\),則()A.\(\complement_{U}A=\{3,4,5\}\)B.\(\complement_{U}B=\{1,5\}\)C.\((\complement_{U}A)\cap(\complement_{U}B)=\{5\}\)D.\((\complement_{U}A)\cup(\complement_{U}B)=\{1,2,3,4\}\)答案:ABCD三、判斷題(每題2分,共10題)1.空集是任何集合的真子集。(）答案：錯2.若\(A\subseteqB\),則\(A\)中的元素都屬于\(B\)。()答案：對3.集合\(\{a,b\}\)的子集有\(zhòng)(\{a\}\),\(\{b\}\),\(\{a,b\}\)。()答案:錯,還有空集\(\varnothing\)4.若\(A\cupB=A\),則\(B\subseteqA\)。（）答案：對5.集合\(\{x|x^{2}+1=0\}\)是空集。()答案：對6.若\(A\capB=B\),則\(B\subseteqA\)。()答案：對7.集合\(\{1,2\}\)和集合\(\{2,1\}\)是不同的集合。()答案：錯8.若全集\(U=\{1,2,3,4\}\),集合\(A=\{1,2\}\),則\(\complement_{U}A=\{3,4\}\)。()答案：對9.集合\(\{x|x\)是有理數(shù)\(\}\)與集合\(\{x|x\)是實數(shù)\(\}\)的交集是\(\{x|x\)是有理數(shù)\(\}\)。()答案：對10.若\(A\subseteqB\),\(B\subseteqC\),則\(A\subseteqC\)。()答案：對四、簡答題(每題5分,共4題)1.已知集合\(A=\{1,2,3\}\),集合\(B=\{2,3,4\}\),求\(A\capB\)和\(A\cupB\)。答案:\(A\capB=\{2,3\}\),\(A\cupB=\{1,2,3,4\}\)。先找出兩個集合中相同的元素得\(A\capB\),再把兩個集合所有元素合并去重得\(A\cupB\)。2.設全集\(U=\{1,2,3,4,5\}\),集合\(A=\{1,3,5\}\),求\(\complement_{U}A\)。答案:\(\complement_{U}A=\{2,4\}\)。在全集\(U\)中去掉集合\(A\)中的元素,剩下的元素組成的集合就是\(\complement_{U}A\)。3.若集合\(A=\{x|x^{2}-2x-3=0\}\),集合\(B=\{-1,3\}\),判斷\(A\)與\(B\)的關(guān)系。答案:解方程\(x^{2}-2x-3=0\)得\((x-3)(x+1)=0\),\(x=3\)或\(x=-1\),所以\(A=\{-1,3\}\),則\(A=B\)。4.已知集合\(A=\{x|x\gt0\}\),集合\(B=\{x|x\lt2\}\),求\(A\capB\)。答案:\(A\capB=\{x|0\ltx\lt2\}\)。取兩個集合中公共部分的\(x\)的取值范圍。五、討論題(每題5分,共4題)1.舉例說明如何判斷兩個集合之間的包含關(guān)系。答案:比如集合\(A=\{1,2\}\),集合\(B=\{1,2,3\}\),\(A\)中的元素\(1\),\(2\)都在\(B\)中,所以\(A\subseteqB\);若集合\(A\)中的元素都在集合\(B\)中且\(B\)中有\(zhòng)(A\)沒有的元素,則\(A\subsetneqqB\)。2.解釋空集在集合運算中的作用。答案:空集是任何集合的子集,在交集運算中,若一個集合與空集相交結(jié)果為空集;在并集運算中,一個集合與空集并集就是該集合本身。例如\(A\cap\varnothing=\varnothing\),\(A\cup\varnothing=A\)。3.當全集\(U\),集合\(A\),\(\complement_{U}A\)已知時,如何求集合\(B\)滿足\(A\subseteqB\subseteqU\)?答案:先確定\(A\)中的元素,然后在全集\(U\)中找包含\(A\)且元素個數(shù)不超過\(U\)的集合。比如\