名校
1 . 设函数
其中P,M是非空数集.记f(P)={y|y=f(x),x∈P},f(M)={y|y=f(x),x∈M}.
(Ⅰ)若P=[0,3],M=(﹣∞,﹣1),求f(P)∪f(M);
(Ⅱ)若P∩M=∅,且f(x)是定义在R上的增函数,求集合P,M;
(Ⅲ)判断命题“若P∪M≠R,则f(P)∪f(M)≠R”的真假,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c2bb74c113b155d0534008a947169.png)
(Ⅰ)若P=[0,3],M=(﹣∞,﹣1),求f(P)∪f(M);
(Ⅱ)若P∩M=∅,且f(x)是定义在R上的增函数,求集合P,M;
(Ⅲ)判断命题“若P∪M≠R,则f(P)∪f(M)≠R”的真假,并加以证明.
您最近一年使用:0次
2020-01-19更新
|
742次组卷
|
5卷引用:北京市西城区2019-2020学年高一上学期期末数学试题2
北京市西城区2019-2020学年高一上学期期末数学试题2北京市第八中学2023-2024学年高一上学期期中练习数学试题北京市和平街第一中学2023-2024学年高一上学期期中考试数学试题北京市昌平区第二中学2023-2024学年高一上学期期中考试数学试题(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
名校
解题方法
2 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-02-01更新
|
577次组卷
|
6卷引用:上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题
上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题上海市曹杨二中2019-2020学年高二上学期期末数学试题上海市七宝中学2020届高三上学期11月月考数学试题北京市东城区景山学校2021届高三上学期期中数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21北京市密云区第二中学2024届高三上学期10月月考数学试题
名校
3 . 已知:集合
,其中
.
,称
为
的第
个坐标分量.若
,且满足如下两条性质:
①
中元素个数不少于
个.
②
,
,
,存在
,使得
,
,
的第
个坐标分量都是
.则称
为
的一个好子集.
(
)若
为
的一个好子集,且
,
,写出
,
.
(
)若
为
的一个好子集,求证:
中元素个数不超过
.
(
)若
为
的一个好子集且
中恰好有
个元素,求证:一定存在唯一一个
,使得
中所有元素的第
个坐标分量都是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04c8d2e5962266734b677842b1985cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd012d9216e34923d1e1a5e1481483e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d05f3a6e0d625cf73bb656dd85f666d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d218f9864db4a589a4778fcb4d23bb32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a86c79fb771a07a413c755e4295b160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f38996525564d196bce79c3fef9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e1862efa4931cbf76743033ad6f1e3.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30814d8d521fc3932d9215abb82afcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a10ccb89e17789ec5ef5d04093c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3342a206b878dd392294c8100a9c73b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5c085395803c2794ea1e5b3d685c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e1862efa4931cbf76743033ad6f1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e1862efa4931cbf76743033ad6f1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c632c1dee2f3849015044acedc50bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
2018-07-02更新
|
521次组卷
|
5卷引用:北京市第二十中学2020-2021学年高二上学期期期末试题
北京市第二十中学2020-2021学年高二上学期期期末试题北京师范大学第二附属中学2017~2018学年度第一学期期中考试高一数学试卷【全国百强校】北京市西城区北京师范大学第二附属中学2017-2018学年高一上学期期中考试数学试题(已下线)卷16-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)北京市中国科学院附属实验学校2021-2022学年高二9月月考数学试题
4 . 已知集合
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
中所有不同值的个数.
(1)若集合
,求
;
(2)若集合
,求证:
的值两两不同,并求
;
(3)求
的最小值.(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ce6be5490570923b903dd8b41af21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34eab5752f27333c8764b320fe5ea92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a6fdf9a72190e86809b49ac0496f7d.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdbe456b157ab21b970a5b59308125b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a17ac17c60f8f287167afce4662b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
5 . 已知q和n均为给定的大于1的自然数.设集合M={0,1,2,…,q-1},
集合A={x|x=x1+x2q+…+xnqn-1,xi∈M,i=1,2,…,n}.
(1)当q=2,n=3时,用列举法表示集合A.
(2)设s,t∈A,s=a1+a2q+…+anqn-1,t=b1+b2q+…+bnqn-1,其中ai,bi∈M,i=1,2,…,n.证明:若an<bn,则s<t.
您最近一年使用:0次
2018-02-02更新
|
405次组卷
|
4卷引用:陕西省黄陵中学高新部2017-2018学年高一上学期期末考试数学试题
陕西省黄陵中学高新部2017-2018学年高一上学期期末考试数学试题(已下线)2019高考备考一轮复习精品资料【理】专题一 集合的概念与运算 教学案(已下线)2019高考热点题型和提分秘籍 【理数】专题1 集合( 教学案)智能测评与辅导[文]-算法、推理与证明(复数)
解题方法
6 . 对于任意的n∈N*,记集合En={1,2,3,…,n},Pn=
.若集合A满足下列条件:①A⊆Pn;②∀x1,x2∈A,且x1≠x2,不存在k∈N*,使x1+x2=k2,则称A具有性质Ω.如当n=2时,E2={1,2},P2=
.∀x1,x2∈P2,且x1≠x2,不存在k∈N*,使x1+x2=k2,所以P2具有性质Ω.
(1)写出集合P3,P5中的元素个数,并判断P3是否具有性质Ω.
(2)证明:不存在A,B具有性质Ω,且A∩B=∅,使E15=A∪B.
(3)若存在A,B具有性质Ω,且A∩B=∅,使Pn=A∪B,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9df41d67a96fb8ffc19bbbcf5597dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2623bcade9e7521db92dfcb45b90f91.png)
(1)写出集合P3,P5中的元素个数,并判断P3是否具有性质Ω.
(2)证明:不存在A,B具有性质Ω,且A∩B=∅,使E15=A∪B.
(3)若存在A,B具有性质Ω,且A∩B=∅,使Pn=A∪B,求n的最大值.
您最近一年使用:0次
7 . 已知集合
,其中
,由
中的元素构成两个相应的集合:
,
.
其中
是有序数对,集合
和
中的元素个数分别为
和
.
若对于任意的
,总有
,则称集合
具有性质
.
(Ⅰ)检验集合
与
是否具有性质
并对其中具有性质
的集合,写出相应的集合
和
.
(Ⅱ)对任何具有性质
的集合
,证明
.
(Ⅲ)判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8213c48030bc2cfa88da0f2a28aca2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d807832357bea22a266e63cbd7e678a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976ed3659749e70adb41abe4030b6ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604a1abd24826ba48fe69d714b1b16d0.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2cacc52ffe015e828a4a5f2fe5ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅰ)检验集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e565001c699e5e221ed616dd7be2bb83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0110544a65399ad66980adc3667b8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(Ⅱ)对任何具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca7597aeef0ed7313f6f78b9658ea5e.png)
(Ⅲ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2016-11-30更新
|
3438次组卷
|
11卷引用:北师大附中2017-2018学年高一下学期期末数学试题1
北师大附中2017-2018学年高一下学期期末数学试题1北师大附中2017-2018学年高一下学期期末数学试题22007年普通高等学校招生全国统一考试理科数学卷(北京)北京东城27中学2018届高三上学期期中考试数学试题上海市大同中学2018-2019学年高一上学期10月学情调研数学试题北京市第二中学2021届高三高考模拟数学试题北京市第十三中学2022届高三上学期开学考数学试题北京市朝阳区北京中学2022-2023学年高一上学期期中数学试题2007 年普通高等学校招生考试数学(理)试题(北京卷)上海市复兴高级中学2021-2022学年高一上学期10月月考数学试题北京名校2023届高三二轮复习 专题三 集合与数列 第3讲 集合与数列创新题