课时分层训练(一)集合A组基础达标(建议用时:30分钟)一、选择题1.(2016·全国卷Ⅱ)已知集合A={1,2,3},B={x|x2<9},则A∩B=()A.{-2,-1,0,1,2,3}B.{-2,-1,0,1,2}C.{1,2,3}D.{1,2}D[∵x2<9,∴-3<x<3,∴B={x|-3<x<3}.又A={1,2,3},∴A∩B={1,2,3}∩{x|-3<x<3}={1,2}.]2.(2015·全国卷Ⅱ)已知集合A={1,2,3},B={2,3},则()A.A=BB.A∩B=∅C.ABD.BAD[∵A={1,2,3},B={2,3},∴2,3∈A且2,3∈B,1∈A但1∉B,∴BA.]3.(2017·潍坊模拟)已知集合A={x|x2-3x+2=0,x∈R},B={x|0<x<5,x∈N},则满足条件A⊆C⊆B的集合C的个数为()【导学号:31222002】A.1B.2C.3D.4D[由x2-3x+2=0,得x=1或x=2,∴A={1,2}.由题意知B={1,2,3,4},∴满足条件的C可为{1,2},{1,2,3},{1,2,4},{1,2,3,4},共4个.]4.(2016·山东高考)设集合A={y|y=2x,x∈R},B={x|x2-1<0},则A∪B=()A.(-1,1)B.(0,1)C.(-1∞,+)D.(0∞,+)C[由已知得A={y|y>0},B={x|-1-1}.]5.(2017·衡水模拟)已知全集U={1,2,3,4,5,6,7,8},集合A={2,3,5,6},集合B={1,3,4,6,7},则集合A∩∁UB=()A.{2,5}B.{3,6}C.{2,5,6}D.{2,3,5,6,8}A[由题意得∁UB={2,5,8},∴A∩∁UB={2,3,5,6}∩{2,5,8}={2,5}.]6.若x∈A,则∈A,就称A是伙伴关系集合,集合M=的所有非空子集中具有伙伴关系的集合的个数是()【导学号:31222003】A.1B.3C.7D.31B[具有伙伴关系的元素组是-1,,2,所以具有伙伴关系的集合有3个:{-1},,.]7.已知全集U=R,A={x|x≤0},B={x|x≥1},则集合∁U(A∪B)=()A.{x|x≥0}B.{x|x≤1}C.{x|0≤x≤1}D.{x|0