1 . 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
名校
2 . 对于正整数集合
,记
,记集合
所有元素之和为
,
.若
,存在非空集合
、
,满足:①
;②
;③
,则称
存在“双拆”.若
,
均存在“双拆”,称
可以“任意双拆”.
(1)判断集合
和
是否存在“双拆”?如果是,继续判断可否“任意双拆”?(不必写过程,直接写出判断结果);
(2)
,证明:
不能“任意双拆”;
(3)若
可以“任意双拆”,求
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ea2881211e9974998bbf1b6fde02ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18092168088b399de1c2d765cc0aad06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/961240074ef9851fe26f93d35cb94adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375fae50ad1b3d14c011673110256fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a82f4f602933ea0b10f9eb8e63ce186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bef6656e3bcaf95b20f06773ee256bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dd183310dbf9e6529405574cefc9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd170c506a8ce70f550f5751ae016ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536709af74dd33236a7dcc13cee3933f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1752a1d13ec6a233405fce4d5af61d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2022-11-04更新
|
571次组卷
|
6卷引用:北京市海淀区中国人民大学附属中学2022-2023学年高一上学期期中练习数学试题
北京市海淀区中国人民大学附属中学2022-2023学年高一上学期期中练习数学试题北京市海淀区二十中学2022-2023学年高一上学期阶段性检测(12月月考)数学试题北京市顺义区第一中学2023-2024学年高一上学期期中考试数学试题北京市第二中学2023-2024学年高一上学期第一学段考试数学试卷(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(人教A版2019必修第一册)(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)
名校
3 . 定义一个n元数组
,其中
或1,i、
﹐设
,
表示A和B中相应的元素不同的个数(例如,
,则
).
(1)若
,写出所有满足
的5元数组B;
(2)设
,记
的5元数组B的个数为
,求
的值;
(3)令
(n个0),
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386216116ecf49be4a0ebdddacec60bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70ee9f169cd7e6d36ddc301f2653498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f436426be5f021a8eebccc2298b6dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1411bda8a6dee80bb6387471cfe945bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092c1c15b9dfe25f62c33a23c63b9df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ece890a7ada4782024dea0f592c14a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aa6b0d8f54fa4ba22615db58834fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b44b19e29782883ea7a17ed0684154.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88e3c1464bf1ec790168779faced2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ce4001c7467ac929dd94288f6bce09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e6bd700ba1c9217f2c2598b459d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c94707f5af06686f6265f2fdaa69b85.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e725c235172819de9751e908e63ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74fb4d2ac68691e607eb7c5cdf418ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc8f86e2046efa8b4f1dd5104b11c8.png)
您最近一年使用:0次
4 . 对于正整数集合
,
,如果去掉其中任意一个元素
之后,剩余的所有元素组成的集合能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,我们就称集合
为“和谐集”
(1)判断集合
是否是“和谐集”,并说明理由.
(2)判断集合
是否是“和谐集”,并说明理由.
(3)求证:集合
不是和谐集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8a2094e3909dbce5d966776a5cb847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2613279bffd089060f0d05e48eabd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42c015b7ebebf921e559369b98bc98d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb62f10c9971d5aafff76dc4dfb4732.png)
(2)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b91f2f906face10cd95d22d83921abc.png)
(3)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b0be0be95b689ebcf3ccdfd059652.png)
您最近一年使用:0次
名校
5 . 设集合
的最大元素为
,最小元素为
,记
的特征值为
,若集合中只有一个元素,规定其特征值为0.已知
,
,
,…,
是集合
的元素个数均不相同的非空真子集,且
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c6ab6d0dc544cc915864198cd9affa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858911660b233271d57b17e358232d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f56b4df8438e8d28c9ed6e747a41cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.10 | B.11 | C.12 | D.13 |
您最近一年使用:0次
18-19高一上·北京·期中
名校
解题方法
6 . 给定数集A,若对于任意a,
,有
,
,则称集合A为闭集合.
(1)判断集合
,
是否为闭集合,并给出证明;
(2)若集合C,D为闭集合,则
是否一定为闭集合?请说明理由;
(3)若集合C,D为闭集合,且
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9df3a17aa370eba2add2c13cfc2619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7459675b810cf0b84696762ffc5c12f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af08c31cb7887fad0ace3ad9fab61dd.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10b6c92b451ea80e63cbefd44c3681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e06607d8d217bce265fe228bd9401c.png)
(2)若集合C,D为闭集合,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84601c1ff9db2761531f127cd020dd59.png)
(3)若集合C,D为闭集合,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6857a6ef1ed2aeba64cd5c6dfd039dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
您最近一年使用:0次
2022-08-28更新
|
2685次组卷
|
16卷引用:【全国百强校】北京市北京第四中学2018-2019学年高一上学期期中考试数学试题
(已下线)【全国百强校】北京市北京第四中学2018-2019学年高一上学期期中考试数学试题北京市第一六一中学2021-2022学年高一上学期期中阶段测试数学试题北京市八一学校2022-2023学年高一上学期10月月考数学试题人教A版(2019) 必修第一册(上) 重难点知识清单 第一章 集合与常用逻辑用语 单元复习测试安徽省阜阳市太和第一中学2020-2021学年高一上学期10月月考数学试题(已下线)第一单元 (综合培优)集合与常用逻辑用语 B卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)河南省林州市第一中学2021-2022学年高一上学期开学检测(普通班)数学试题(已下线)第一章 集合与常用逻辑用语章末测试(章末测试)-【上好课】2021-2022学年高一数学同步备课系列(人教A版2019必修第一册)(已下线)专题1.12 集合与常用逻辑用语 全章综合测试卷-提高篇北师大版(2019) 必修第一册 名校名师卷 专题一 集合与常用逻辑用语2023版 苏教版(2019) 必修第一册 名校名师卷 专题一 集合与常用逻辑用语苏教版(2019) 必修第一册 突围者 第1章 章末培优专练集合新定义题型专练2023版 湘教版(2019) 必修第一册 名师精选卷 第一章 集合与常用逻辑用语湖北省十堰市天河英才高中2022-2023学年高一上学期9月月考数学试题(已下线)专题01 含参数与新定义的集合问题-2022-2023学年高一数学新教材同步配套教学讲义(苏教版2019必修第一册)
7 . 已知集合
.对集合
中的任意元素
,定义
,当正整数
时,定义
(约定
).
(1)若
,
,求
和
;
(2)若
满足
且
,求
的所有可能结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0f481e1095b418d12e897e921fa65a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c644f3743ecaa6c2b6597bf3822d1041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88c33889aa781ac5d60ed7a4a687b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175200f968fc2a6a18f25f2dac491e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f88776c6c89617192c501dc7f5c9b46.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc8c0937f96c05fc90f6ee823eda0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae510893b3f224d48be991b9167b6a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9e226d8678f9599f4a5b81ca6cbe73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5101a4ab2f5c09c8d3bb12805160b0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c644f3743ecaa6c2b6597bf3822d1041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb07afe5d964479865b849c7e71da61d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade88bfc9e924640d0263447b2cbf8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
8 . 对于正整数集合
,如果去掉其中任意一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“和谐集”.
(1)判断集合
与
是否为“和谐集”(不必写过程);
(2)求证:若集合
是“和谐集”,则集合
中元素个数为奇数;
(3)若集合
是“和谐集”,求集合
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1e8da4ab7ad3bf25dccde55559c16b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee470d0232b6b37f2fb2ab15aae0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b07a67307d5d4627efa688b30e5573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9afb9e20afd1670de12af12a2aa32f9.png)
(2)求证:若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2022-06-13更新
|
1441次组卷
|
10卷引用:北京市第二中学2021-2022学年高一6月阶段落实测试数学试题
北京市第二中学2021-2022学年高一6月阶段落实测试数学试题北京理工大学附属中学2022-2023学年高一上学期10月月考数学试题北京市顺义区第一中学2023-2024学年高一上学期12月月考数学试题第1章 集合 单元综合测试卷第一章 集合(B卷·能力提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第一册)第一章 集合(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第一册)第一章 集合与常用逻辑用语(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(人教A版2019必修第一册)江苏省扬州市高邮市第一中学2022-2023学年高一上学期期初数学试题(已下线)第02讲 集合的运算(7大考点13种解题方法)-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)第1章 集合与常用逻辑用语-【高中数学课堂】单元测试能力卷(人教B版2019)
9 . 对于任意的
,记集合
,
,若集合A满足下列条件:①
;②
,且
,不存在
,使
,则称A具有性质Ω.如当
时,
,
,
,且
,不存在
,使
,所以
具有性质Ω.
(1)写出集合
,
中的元素个数,并判断
是否具有性质Ω.
(2)证明:不存在A、B具有性质Ω,且
,使
.
(3)若存在A、B具有性质Ω,且
,使
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6136140ae3eda80fa2251dd6f3840415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d61ab4e28840d2597566a9677cf1670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8a4824db78a0f34777372e4cb7ff9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac5230b93cc884fe3b8798d0cd2f30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b354b577ec9cdb8941ba4f7b66a8aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba1217bdce7fed00b4c488ae2d1c83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1922efd1e913d2721fbf240ea3740ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d64a4f7b1f0fb56b37f75d95a50d321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b354b577ec9cdb8941ba4f7b66a8aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)证明:不存在A、B具有性质Ω,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef35a92301f139a035fc643ff1545c1.png)
(3)若存在A、B具有性质Ω,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a347c4b63fad850a75f36e87f44c86.png)
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2022-04-09更新
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5卷引用:北京市清华大学附属中学朝阳学校2021-2022学年高一3月质量检测数学试题
北京市清华大学附属中学朝阳学校2021-2022学年高一3月质量检测数学试题重庆市南开中学高2022-2023学年高一上学期第一次月考数学试题(已下线)1.3 交集、并集(2)(已下线)第02讲 集合的运算(7大考点13种解题方法)-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)高一上学期期中考试解答题压轴题50题专练-举一反三系列
名校
10 . 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:
,并指出等号成立的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6040700d8c0d30470a38d233c12f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cbf041bb12004891be66236a427bf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9ca84aa3597da3531ac4c175d94147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18db8b768e5060b3471415e4b55ac30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaa284b3d0dce4256ded57204703c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a236fe66ea4ef97f3cba08affdb9de.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/c078203503613eb6dab717ffe1e513a2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3d724a3e6f93bc0be9957d94bf30ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8dcc2ae480c1fdba0d4b89922a355f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8d6cf178ab517dc7e27523be5321d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0628c5791b48f147759f9f4a72e90f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa2160591c654883f613e6dcd9851d6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cbf041bb12004891be66236a427bf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6040700d8c0d30470a38d233c12f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32da979e212a228284f556eb51cc96f2.png)
您最近一年使用:0次
2022-03-24更新
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6卷引用:北京市清华大学附属中学朝阳学校2021-2022学年高一5月月考数学试题