名校
1 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
,
,
,对任意
,定义
.若存在正整数
,使得对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
,都有
,则称集合
具有性质
.如集合
、
都具有性质
.记
是集合
中的最大值.
(1)判断集合
和集合
是否具有性质
(直接写出结论);
(2)若集合
具有性质
,求证:
和
;
(3)若集合
具有性质
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ef42f964d02549eec898b0d3f0588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e326e8f60f19e64e32c584ccfc40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a703c80c9a9624b08ada02523257b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ff43ffdcc8b03787a1faa6509d79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db67bc808e5b3a6ba3f7691a50d20957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20362ac95ee78ef94caeb0579bb40bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1baf30f84a1797c8e345c624e6cab1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10cda3e056f1db8777f3c322165bb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be13762bee8c87a904b93379c76ac8b.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d9e9e68d8fa416188fe9c5efafae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2309c5526d918b1e6d456a999ab88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e296d9adecd44ddd36ec145dcf9dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f80a1f6a8c236559e2fa55feb9ee1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923eed4cf08e8bef3e7a61ce3ba48d62.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b97c217370c2b3d22e6738006cc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d5ade4406641db15a62630f06e4201.png)
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2022-12-26更新
|
424次组卷
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4卷引用:第1章 集合与逻辑 单元测试(单元重点)--高一数学同步精品课堂(沪教版2020必修第一册)
(已下线)第1章 集合与逻辑 单元测试(单元重点)--高一数学同步精品课堂(沪教版2020必修第一册)上海师范大学附属中学闵行分校2023-2024学年高一上学期期中数学试题上海市曹杨第二中学2021-2022学年高一上学期期中数学试题广西名校2024届高三高考模拟猜题试卷
名校
2 . 已知集合
(
且
),
,且
.若对任意
,
,当
时,存在
,使得
,则称
是
的
元完美子集.
(1)判断下列集合是否是
的3元完美子集,并说明理由;
①
;
②
;
(2)若
是
的3元完美子集,求
的最小值;
(3)若
是
(
且
)的
元完美子集,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410a811a99d6f15164cdda4597323168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dd50a4fd2329323aa21597e8ff664b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aadf01e5fac133cf390407bfad26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d169a02afabbe304cf64b355bf71742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49972f77c4c3b89116f02cbaba7f9089.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc21b9d3aa5f307d9c9d63ffaf68dc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfbdcd7014f79de428c1d5e6525aecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0604cb71df25c9b90c5d7521d3edd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717995559c925685dacedc60be48fd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7c557b1aadac2ee7012fb1e1ba5f8.png)
您最近一年使用:0次
2022-05-12更新
|
738次组卷
|
4卷引用:专题16 数列新定义题的解法 微点2 数列新定义题综合训练
(已下线)专题16 数列新定义题的解法 微点2 数列新定义题综合训练北京市第二中学2022—2023学年高一下学期第六学段阶段性考试数学试题北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题重庆市杨家坪中学2022-2023学年高一上学期10月月考数学试题
名校
3 . 已知集合
具有性质
:对任意
,
(
),
与
至少一个属于
.
(1)分别判断集合
,与
是否具有性质
,并说明理由;
(2)证明:
;
(3)
具有性质
,当
时,求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45a296e38b585f04206530b9e53d36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18db8b768e5060b3471415e4b55ac30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b42882dd156f60b1bbcc394155ee88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9bf9b7e8523d5cdca10de9ae70770e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2faf3937abcb6a59071c17bc6bb10f6.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d020cd453031ae9eede7961ec78f21a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2022-11-08更新
|
310次组卷
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3卷引用:广东省广州市第一一三中学2023-2024学年高一上学期9月月考数学试题
4 . 定义两个非空数集
的“和集”为
,对有限集合
,记
.
(1)已知
,
,求出
与
;
(2)任取非空有限数集
,证明:
;
(3)
的非空子集
满足:
,都有
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c7a43079a55f6a53b1307b2b04b55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f89b4b3ad484893d998c581ad24556.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dab17f641ff493bf06551cb038cab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80d440b9478c09a6870403a8bd5cf38.png)
(2)任取非空有限数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a48c70e8d0da803583934a9fd362915.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bdeca2b562c73695cd1f5139b4d2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e532310f27fb7f3550c55c596dda168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8063f81dccffca2ca76e183bda91d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a90b4472c17fe6f9998088960a72a6.png)
您最近一年使用:0次
5 . 若集合
,其中
为非空集合,
,则称集合
为集合A的一个n划分.
(1)写出集合
的所有不同的2划分;
(2)设
为有理数集Q的一个2划分,且满足对任意
,任意
,都有
.则下列四种情况哪些可能成立,哪些不可能成立?可能成立的情况请举出一个例子,不能成立的情况请说明理由;
①
中的元素存在最大值,
中的元素不存在最小值;
②
中的元素不存在最大值,
中的元素存在最小值;
③
中的元素不存在最大值,
中的元素不存在最小值;
④
中的元素存在最大值,
中的元素存在最小值.
(3)设集合
,对于集合A的任意一个3划分
,证明:存在
,存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e887bc41e7c72b69482b7cb153b9f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c7bb3662baf8ab4da46099adc0180a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c5b1cefd28f020a899803181867be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a111d44296a6d4c373e33e0267baeb8.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b064529d4274a25ea70cec901689595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c303b55101c9d049947443d85bd3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b31852ebf26c81693dc084facc76a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a99ef56247036a98e53aa8c16c3e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48ec13d90542aaca7af71224a3d8ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2199afe5dd5ad25962537abfa209b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f351ce8d2e5f2160bf2f771642f6dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92916a0ce7c44bbd09a54a9aedd2e8ac.png)
您最近一年使用:0次
2022-07-08更新
|
1254次组卷
|
6卷引用:北京市海淀区首都师范大学附属中学2023-2024学年高一上学期10月期中练习数学试题
北京市海淀区首都师范大学附属中学2023-2024学年高一上学期10月期中练习数学试题北京市第一七一中学2023-2024学年高一上学期12月调研数学试题(已下线)第1章 集合与常用逻辑用语-【优化数学】单元测试能力卷(人教B版2019)北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题(已下线)第1章 集合与常用逻辑用语(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)高一上学期期末【压轴60题考点专练】-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
名校
解题方法
6 . 设集合A的元素都是正整数,满足如下条件:①A的元素个数不小于3;②若
,则
的所有因数都属于A;③若
,
,
,则
,请回答下面的问题:
(1)证明:1,2,3,4,5都是集合A的元素
(2)判断2021是否集合A的元素,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9df3a17aa370eba2add2c13cfc2619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63478e7cf55bad51bbd4ce1e23363e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad767600de4c7c7d2fa23bd2c2813f.png)
(1)证明:1,2,3,4,5都是集合A的元素
(2)判断2021是否集合A的元素,并说明理由
您最近一年使用:0次
名校
7 . 对于任意有限集S,T,定义集合
,
表示S的元素个数.已知集合A,B为实数集R的非空有限子集,设集合
.
(1)若
,求集合C及其元素个数
;
(2)若
,求
的值;
(3)已知D为有限集,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c2770eb8c85bdc511221637c16e0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44307573cc59d670ca1f6d02593b83f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3518dc47ae1c0534092ca302a730472e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed1774cd6b193026d3391cefa689310.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c0a712c58633fb214b1c405efe992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5901b6ae6466abfd6c323bdeeadd6c99.png)
(3)已知D为有限集,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680d51970e92b92342223af8b37d4a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05ed8035ddd31bc242af5a52e9e8a08.png)
您最近一年使用:0次
2022-09-06更新
|
483次组卷
|
5卷引用:期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)
(已下线)期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)新疆乌鲁木齐天山区2023-2024学年高一上学期第一次阶段性测试数学试题(一)上海市建平中学2021-2022学年高一上学期期中数学试题(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)高一上学期期中【压轴60题考点专练】(必修一前三章)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
8 . 已知数集
具有性质P:对任意的
,使得
成立.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)已知
,求证:
;
(3)若
,求数集A中所有元素的和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b7edfe73bdd0bb2a6e84512b62bdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a921d157d198de0f934da07e16dc7df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59970351aa04d29f62d480c7280763e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a3069c8accda13019e775a5dc198c2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108bce68aab5565c4ed9a0c3e11150e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7006f52b1f7cf1bdf8374bd2da3e4562.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
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2022-05-13更新
|
1012次组卷
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7卷引用:第01节 集合(好题帮)
9 . 设
,
,…,
,
,是
个互不相同的闭区间,若存在实数
使得
,则称这
个闭区间为聚合区间,
为该聚合区间的聚合点.
(1)已知
,
为聚合区间,求t的值;
(2)已知
,
,…,
,
为聚合区间.
(ⅰ)设
,
是该聚合区间的两个不同的聚合点.求证:存在k,
,使得
;
(ⅱ)若对任意p,q(
且p,
),都有
,
互不包含.求证:存在不同的i,
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d109268e15e8f04f94a6155e9432043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5843978e1e20fb7a901143839741cbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fac9603f08a2388999d33306b7047b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12100db597992af7e546de75b4d3605b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff40cfd1abdbc307e21f7c8ba502b16b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a12c01aaf24489a3285afd2ab6a7bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b54084cc62f8edcc4cce1b1ffb8b13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7196435048015ab9fa4f9f90caf55e26.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d109268e15e8f04f94a6155e9432043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac4f4a5794941d335325cc5f1dd6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fac9603f08a2388999d33306b7047b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12100db597992af7e546de75b4d3605b.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725dde58532f70e91baeb9ff90519c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d5b9ef2dcd314f0d85adeb77675558.png)
(ⅱ)若对任意p,q(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14e88b76e8fbfed5a6b57a9e708fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb953277188ba4f8b6511174f4c4081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f392d06cbc33ac357d3478a543ce030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20895209100403cf486bc9413889f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70216275cb366804f695c4cf54b0798f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba4514bef9609e94f709466af7091db.png)
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2022-04-27更新
|
1102次组卷
|
6卷引用:第01节 集合(好题帮)
(已下线)第01节 集合(好题帮)(已下线)专题01 集合与常用逻辑用语(讲义)-2023年高考数学一轮复习精讲精练宝典(新高考专用)北京市首都师范大学附属丽泽中学2023届高三下学期2月月考数学试题北京卷专题18数列(解答题)北京卷专题02集合(解答题)北京市丰台区2022届高三高考二模数学试题
10 . 设
且
,集合
,若对
的任意
元子集
,都存在
,满足:
,
,且
为偶数,则称
为理想集,并将
的最小值记为
.
(1)当
时,是否存在理想集?若存在,求出相应的
;若不存在,请说明理由;
(2)当
时,是否存在理想集?若存在,直接写出对应的
以及满足条件的
;若不存在,请说明理由;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179de8d0ec06e96b2fa0ac16ede34e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76fbcfa1d6ec3bec5f131a8c953a705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd28f29074d36b6721a929eb217f9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf538440bd45e5881f2b22994560ba7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae24688d4c45aad43e9af0b7bbfda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76fbcfa1d6ec3bec5f131a8c953a705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76fbcfa1d6ec3bec5f131a8c953a705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b58ca66d3e9ac1283703b5063ac9bea.png)
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