《集合》专项练习参考答案
1.(2016全国Ⅰ卷,文1,5分)设集合{1,3,5,7}A =,{|25}B x x =≤≤,则A ∩B =( ) (A ){1,3} (B ){3,5} (C ){5,7} (D ){1,7}
【解析】集合A 与集合B 的公共元素有3,5,故}5,3{=B A ,故选B .
2.(2016全国Ⅱ卷,文1,5分)已知集合{123}A =,,,2{|9}B x x =<,则A ∩B =( ) (A ){210123}--,,,,, (B ){21012}--,
,,, (C ){123},,
(D ){12}, 【解析】由29x <得33x -<<,所以{|33}B x x =-<<,因为{1,2,3}A =,所以
{1,2}A B =,故选D .
3.(2016全国Ⅲ卷,文1,5分)设集合{0,2,4,6,8,10},{4,8}A B ==,则A B =( )
(A ){48}, (B ){026},, (C ){02610},,, (D ){0246810},
,,,, 【解析】由补集的概念,得
{0,2,6,10}A
B =,故选
C .
4.(2016全国Ⅰ卷,理1,5分)设集合2{|430}A x x x =-+<,{|230}B x x =->, 则A ∩B =( )
(A )3
(3,)2-- (B )3(3,)2- (C )3(1,)2 (D )3(,3)2
【解析】对于集合A :解方程x 2-4x +3=0得,x 1=1,x 2=3,所以A ={x |1<x <3}(大于取两边,小于取中间).对于集合B :2x -3>0,解得x >
23
.3{|3}2
A B x x ∴=<<.选D .
5.2016全国Ⅱ卷,理1,5分)已知(3)(1)i z m m =++-在复平面内对应的点在第四象限,则实数m 的取值范围是( )
(A )(31)
-, (B )(13)-,(C )(1,)∞+(D )(3)∞--, 【解析】要使复数z 对应的点在第四象限,应满足30
10m m +>??-
,解得31m -<<,故选A .
6.(2016全国Ⅲ卷,理1,5分)设集合{}{}
(x 2)(x 3)0,T 0S x x x =--≥=>,则S ∩T =( )
(A) [2,3] (B)(-∞ ,2] [3,+∞)
(C) [3,+∞) (D)(0,2] [3,+∞)
7.(2016北京,文1,5分)已知集合{|24},{|3>5}A x x B x x x =<<=<或,则A
B =( )
(A ){|2<<5}x x (B ){|<45}x x x >或 (C ){|2<<3}x x (D ){|<25}x x x >或
【解析】画数轴得,6
234510
,所以(2,3)A
B =,故选
C .
8.(2016北京,理1,5分)已知集合{|||2}A x x =<,{1,0,1,2,3}B =-,则A B =( ) (A ){0,1}(B ){0,1,2}(C ){1,0,1}-(D ){1,0,1,2}-
【解析一】对于集合A :(解绝对值不等的常用方法是两边同时平方)|x |<2,两边同时平方得x 2<4,解方程x 2=4得,x 1=-2,x 2=2,所以A ={x |-2<x <2}(大于取两边,小于取中间).所以A ∩B ={-1,0,1}.故选C .
【解析二】对于集合A :(绝对值不等式解法二:|x |<2?-2<x <2).A ={x |-2<x <2}.所以A ∩B ={-1,0,1}.故选C . 9.(2016上海,文理1,5分)设x ∈R ,则不等式31x -<的解集为_______. 【答案】(24),
【解析】试题分析:421311|3|<<-<-?<-x x x ,故不等式1|3|<-x 的解集为)4,2(.
【解析一】对不等式31x -<:(解绝对值不等的常用方法是两边同时平方)|x -3|<1,两边同时平方得(x -3)2<1,解方程(x -3)2=1得,x 1=2,x 2=4,所以A ={x |2<x <4}. 【解析二】对于集合A :(绝对值不等式解法二:|x -3|<1?-1<x -3<1,解得2<x <4).A ={x |2<x <4}. 10.(2016山东,文1,5分)设集合{1,2,3,4,5,6},{1,3,5},{3,4,5}U A B ===,则()U A B =
(A ){2,6} (B ){3,6} (C ){1,3,4,5} (D ){1,2,4,6} 【答案】A
11.(2016山东,理2,5分)设集合2{|2,},{|10},x A y y x B x x ==∈=- (A )(1,1)- (B )(0,1) (C )(1,)-+∞ (D )(0,)+∞ 【答案】C 【解析】对于集合A :∵y =2x >0,∴A ={y |y >0}.对于集合B :∵x 2-1=0,解得x =±1,∴B ={x |-1<x <1}(大于取两边,小于取中间).∴A ∪B =(1,)-+∞ 12.(2016四川,文2,5分)设集合A ={x |1≤x ≤5},Z 为整数集,则集合A∩Z 中元素的个数是 (A)6 (B)5 (C)4 (D)3 【答案】B 【解析】{1,2,3,4,5}A =Z ,由Z 为整数集得Z ={…-3,-2,-1,0,1,2,3…}.故 A Z 中元素的个数为5,选 B . 13.(2016四川,理1,5分)设集合{|22}A x x =-≤≤,Z 为整数集,则A Z 中元素的个数 是( ) (A )3(B )4(C )5(D )6 【答案】C 【解析】由题意,知{2,1,0,1,2}A =--Z ,由Z 为整数集得Z ={…-3,-2,-1,0,1,2,3…}.故A Z 中元素的个数为5,选C . 14.(2016天津,文1,5分)已知集合}3,2,1{=A ,},12|{A x x y y B ∈-==,则A B = (A )}3,1{ (B )}2,1{ (C )}3,2{ (D )}3,2,1{ 【答案】A 【解析】∵},12|{A x x y y B ∈-==,∴当x =1时,y =2×1-1=1;当x =2时,y =2×2-1=3;当x =3时,y =2×3-1=5.∴{1,3,5},{1,3}B A B ==.选A . 15.(2016天津,理1,5分)已知集合}{ 4,3,2,1=A ,} {A x x y y B ∈-==,23,则=B A (A )}{ 1 (B )}{4 (C )}{ 3,1 (D )}{4,1 【答案】D 【解析】∵} {A x x y y B ∈-==,23,∴当x =1时,y =3×1-2=1;当x =2时,y =3×2-2=4;当x =3时,y =3×3-2=7;当x =4时,y =4×3-2=10. ∴{14710}{14}B =A B =,,,,,.选D . 16.(2016浙江,文1,5分)已知全集U ={1,2,3,4,5,6},集合P ={1,3,5},Q ={1, 2,4},则U P Q ()=( ) A .{1} B .{3,5} C .{1,2,4,6} D .{1,2,3,4,5} 【答案】C 17.(2016浙江,理1,5分)已知集合P =,Q = ,则P = ( ) A .[2,3] B .(-2,3] C .[1,2) D . 【答案】B 【解析】对于集合Q :∵x 2=4,解得x =±2,∴B ={x |x ≤-2或x ≥2}(大于取两边,小于取中间). 18.(2016江苏,文理1,5分)已知集合{1,2,3,6},{|23},A B x x =-=-<<则=A B _______. 【答案】{}1,2- 【解析】{} {}{}1,2,3,6231,2A B x x =--<<=-.故答案应填:{}1,2- 19.(2015全国Ⅰ卷,文1,5分)已知集合A ={x |x =3n +2,n∈N},B ={6,8,10,12,14}, 则集合A∩B 中元素的个数为( ) A .5 B .4 C .3 D .2 【答案】D 【解析】由已知得A={2,5,8,11,14,17,…},又B={6,8,10,12,14},所以A∩B ={8,14}. 20.(2015全国Ⅱ卷,文1,5分)已知集合A={x|-1<x<2},B={x|0<x<3},则A∪B=( ) A.(-1,3) B.(-1,0) C.(0,2) D.(2,3) 【答案】A 【解析】因为A=(-1,2),B=(0,3),所以A∪B=(-1,3),故选A. 21.(2014全国Ⅰ卷,文1,5分)已知集合M={x|-1<x<3},N={x|-2<x<1},则M∩N =( ) A.(-2,1) B.(-1,1) C.(1,3) D.(-2,3) 【答案】B 【解析】M∩N={x|-1<x<3}∩{x|-2<x<1}={x|-1<x<1}. 22.(2014全国Ⅱ卷,文1,5分)已知集合A={-2,0,2},B={x|x2-x-2=0},则A∩B=( ) A.B.{2} C.{0} D.{-2} 【答案】B 【解析】∵集合A={-2,0,2},B={x|x2-x-2=0}={2,-1},∴A∩B={2},故选B.23.(2013全国Ⅰ卷,文1,5分)已知集合A={1,2,3,4},B={x|x=n2,n∈A},则A∩B =( ) A.{1,4} B.{2,3} C.{9,16} D.{1,2} 【答案】A 【解析】∵B={x|x=n2,n∈A}={1,4,9,16},∴A∩B={1,4},故选A.24.(2013全国Ⅱ卷,文1,5分)已知集合M={x|-3<x<1},N={-3,-2,-1,0,1},则M∩N=( ) A.{-2,-1,0,1} B.{-3,-2,-1,0} C.{-2,-1,0} D.{-3,-2,-1} 【答案】C 【解析】由题意得M∩N={-2,-1,0}.选C. 25.(2012全国卷,文1,5分)已知集合A={x|x2-x-2<0},B={x|-1<x<1},则( )(A)A B(B)B A(C)A=B(D)A∩B= 【答案】B 【解析】A={x|-1<x<2},B={x|-1<x<1},则B A,故选B. 26.(2011全国卷,文1,5分)已知集合M={0,1,2,3,4},N={1,3,5},P=M∩N,则P的子集共有( ) A.2个B.4个C.6个D.8个 【答案】B 【解析】由题意得P=M∩N={1,3},∴P的子集为?,{1},{3},{1,3},共4个. 27.(2010全国卷,文1,5分)已知集合2,,| 4,|A x x x R B x x Z =≤∈=≤∈,则A B = (A )(0,2)(B )[0,2](C )|0,2|(D )|0,1,2| 【解析】{}|22,{0,1,2}A x x B =-≤≤=,{}0,1,2A B =,选D 28.(2009全国卷,文2,5分)设集合A ={4,5,7,9},B ={3,4,7,8,9},全集U A B =, 则集合 ()U A B 中的元素共有( ) (A)3个 (B )4个 (C )5个 (D )6个 【解析】{3,4,5,7,8,9}A B =,{4,7,9}(){3,5,8}U A B A B =∴=.故选A . 29.(2008全国卷,文1,5分)已知集合M ={x |(x +2)(x -1)<0},N ={x |x +1<0},则M∩N=( ) A.(-1,1) B.(-2,1) C.(-2,-1) D.(1,2) 【答案】C 【解析】易求得{}{}|21,|1=-<<=<-M x x N x x ∴{}|21=-<<-M N x x 30.(2007全国卷,文1,5分)设{|210}S x x =+>,{|350}T x x =-<,则S T ?= A .? B .1{|}2x x < C .5{|}3x x > D .15 {|}23 x x -<< 【答案】D . 如有侵权请联系告知删除,感谢你们的配合!