2025年集合简单测试题及答案

2025年集合简单测试题及答案本文借鉴了近年相关经典测试题创作而成，力求帮助考生深入理解测试题型，掌握答题技巧，提升应试能力。一、测试题1.填空题(1)设集合\(A=\{x\mid-1\leqx\leq2\}\)，集合\(B=\{x\midx>1\}\)，则\(A\capB\)=_______。(2)集合\(C=\{1,2,3,4,5\}\)，集合\(D=\{2,4,6\}\)，则\(C-D\)=_______。(3)若集合\(E=\{x\midx^2-3x+2=0\}\)，则\(E\)=_______。(4)设集合\(F=\{x\midx\in\mathbb{Z},-3\leqx\leq3\}\)，则\(F\)=_______。(5)集合\(G=\{x\midx=2k,k\in\mathbb{Z}\}\)，集合\(H=\{x\midx=3k,k\in\mathbb{Z}\}\)，则\(G\capH\)=_______。2.选择题(1)设集合\(P=\{x\midx\text{是偶数}\}\)，集合\(Q=\{x\midx\text{是奇数}\}\)，则\(P\cupQ\)等于：A.\(\mathbb{Z}\)B.\(\emptyset\)C.\(\{0\}\)D.\(\{1\}\)(2)设集合\(A=\{x\midx\geq0\}\)，集合\(B=\{x\midx<0\}\)，则\(A\cupB\)等于：A.\(\mathbb{R}\)B.\(\emptyset\)C.\(\{0\}\)D.\(\{1\}\)(3)设集合\(M=\{x\midx^2=1\}\)，集合\(N=\{1,2\}\)，则\(M\capN\)等于：A.\(\{1\}\)B.\(\{2\}\)C.\(\{1,2\}\)D.\(\emptyset\)(4)设集合\(X=\{x\midx\text{是正整数}\}\)，集合\(Y=\{x\midx\text{是负整数}\}\)，则\(X\cupY\)等于：A.\(\mathbb{Z}\)B.\(\emptyset\)C.\(\{0\}\)D.\(\{1\}\)(5)设集合\(U=\{x\midx\text{是实数}\}\)，集合\(V=\{x\midx\text{是有理数}\}\)，则\(U-V\)等于：A.\(\mathbb{R}\)B.\(\emptyset\)C.\(\{0\}\)D.\(\{x\midx\text{是无理数}\}\)3.解答题(1)设集合\(A=\{x\midx^2-5x+6=0\}\)，集合\(B=\{x\midx<3\}\)，求\(A\capB\)和\(A\cupB\)。(2)设集合\(C=\{x\midx\text{是小于10的正偶数}\}\)，集合\(D=\{x\midx\text{是小于10的正奇数}\}\)，求\(C\cupD\)和\(C\capD\)。(3)设集合\(E=\{x\midx\text{是小于20的质数}\}\)，集合\(F=\{x\midx\text{是小于20的合数}\}\)，求\(E\cupF\)和\(E\capF\)。(4)设集合\(G=\{x\midx\text{是小于100的偶数}\}\)，集合\(H=\{x\midx\text{是小于100的奇数}\}\)，求\(G\cupH\)和\(G\capH\)。(5)设集合\(I=\{x\midx\text{是小于50的平方数}\}\)，集合\(J=\{x\midx\text{是小于50的立方数}\}\)，求\(I\cupJ\)和\(I\capJ\)。二、答案1.填空题(1)\(A\capB=\{x\mid1<x\leq2\}\)(2)\(C-D=\{1,3,5\}\)(3)\(E=\{1,2\}\)(4)\(F=\{-3,-2,-1,0,1,2,3\}\)(5)\(G\capH=\{x\midx=6k,k\in\mathbb{Z}\}\)2.选择题(1)A.\(\mathbb{Z}\)(2)A.\(\mathbb{R}\)(3)D.\(\emptyset\)(4)A.\(\mathbb{Z}\)(5)D.\(\{x\midx\text{是无理数}\}\)3.解答题(1)\(A=\{x\midx^2-5x+6=0\}=\{2,3\}\)\(B=\{x\midx<3\}\)\(A\capB=\{2\}\)\(A\cupB=\{x\midx\leq3\}\)(2)\(C=\{2,4,6,8\}\)\(D=\{1,3,5,7,9\}\)\(C\cupD=\{1,2,3,4,5,6,7,8,9\}\)\(C\capD=\emptyset\)(3)\(E=\{2,3,5,7,11,13,17,19\}\)\(F=\{4,6,8,9,10,12,14,15,16,18\}\)\(E\cupF=\{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19\}\)\(E\capF=\emptyset\)(4)\(G=\{0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48\}\)\(H=\{1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49\}\)\(G\cupH=\{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49\}\)\(G\capH=\emptyset\)(5)\(I=\{0,1,4,9,16,25\}\)\(J=\{0,1\}\)\(I\