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.(2017·天津高考)设集合A={1,2,6},B={2,4},C={1,2,3,4},则(A∪B)∩C =( )
A.{2} B.{1,2,4}
C.{1,2,4,6} D.{1,2,3,4,6}
B [∵A∪B={1,2,6}∪{2,4}={1,2,4,6},
∴(A∪B)∩C={1,2,4,6}∩{1,2,3,4}={1,2,4}.
故选B.]
2.(2017·山东高考)设集合M={x||x-1|<1},N={x|x<2},则M∩N=( ) A.(-1,1) B.(-1,2)
C.(0,2) D.(1,2)
C [∵M={x|0<x<2},N={x|x<2},
∴M∩N={x|0<x<2}∩{x|x<2}={x|0<x<2}.故选C.]
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( )
A.1 B.2
C.3 D.4
D [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|x 2-1<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<x<1},则A ∪B ={x|x>-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 ∩∁U B =( ) 【00090002】
A .{2,5}
B .{3,6}
C .{2,5,6}
D .{2,3,5,6,8}
A [由题意得∁U
B ={2,5,8},
∴A ∩∁U B ={2,3,5,6}∩{2,5,8}={2,5}.]
6.(2018·西安模拟)已知集合M ={-1,0,1},N ={x|x =ab ,a ,b ∈M ,且a ≠b},则集合M 与集合N 的关系是( )
A .M =N
B .M ∩N =N
C .M ∪N =N
D .M ∩N =∅ B [由题意知N ={-1,0},则M ∩N =N ,故选B.]
7.若x ∈A ,则1x ∈A ,就称A 是伙伴关系集合,集合M =⎩⎪⎨⎪⎧⎭
⎪⎬⎪⎫-1,0,12,2,3的所有非空子集中具有伙伴关系的集合的个数是( )
A .1
B .3
C .7
D .31
B [具有伙伴关系的元素组是-1,12
,2,所以具有伙伴关系的集合有3个:{-1},⎩⎪⎨⎪⎧⎭⎪⎬⎪⎫12,2,⎩⎪⎨⎪⎧⎭
⎪⎬⎪⎫-1,12,2.] 二、填空题
8.已知集合A ={x|x 2-2 017x +2 016<0},B ={x|x <a},若A ⊆B ,则实数a 的取值范围是________.
[2 016,+∞) [由x 2-2 017x +2 016<0,解得1<x <2 016,
故A ={x|1<x <2 016},
又B ={x|x <a},A ⊆B ,如图所示,
可得a ≥2 016.]
9.(2016·天津高考)已知集合A ={1,2,3,4},B ={y|y =3x -2,x ∈A},则A ∩B =________.
{1,4} [因为集合B 中,x ∈A ,所以当x =1时,y =3-2=1;
当x =2时,y =3×2-2=4;
当x =3时,y =3×3-2=7;
当x =4时,y =3×4-2=10.
即B ={1,4,7,10}.
又因为A ={1,2,3,4},所以A ∩B ={1,4}.]
10.集合A ={x|x <0},B ={x|y =lg[x(x +1)]},若A -B ={x|x ∈A ,且x ∉B},则A -B =________.
[-1,0) [由x(x +1)>0,得x <-1或x >0,。