1 . 设n为正整数,集合A=
.对于集合A中的任意元素
和
,记
M(
)=
.
(Ⅰ)当n=3时,若
,
,求M(
)和M(
)的值;
(Ⅱ)当n=4时,设B是A的子集,且满足:对于B中的任意元素
,当
相同时,M(
)是奇数;当
不同时,M(
)是偶数.求集合B中元素个数的最大值;
(Ⅲ)给定不小于2的n,设B是A的子集,且满足:对于B中的任意两个不同的元素
,M(
)=0.写出一个集合B,使其元素个数最多,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6a82732fba704672a8e64161f577f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556a481809009382b48169a908a8d3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6b04e179e843c646481aff8f08534d.png)
M(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93273e518df8b4f5344aad520c1ed5c1.png)
(Ⅰ)当n=3时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac43bb35c810a5292cef2e0cab9a59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b682e6511fb6575f4e3ced056e70b170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2803b5392b96e9a91a13bdf57cae37c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
(Ⅱ)当n=4时,设B是A的子集,且满足:对于B中的任意元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
(Ⅲ)给定不小于2的n,设B是A的子集,且满足:对于B中的任意两个不同的元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
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29卷引用:2018年全国普通高等学校招生统一考试理科数学(北京卷)
2018年全国普通高等学校招生统一考试理科数学(北京卷)(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)2019年上海市进才中学高三上学期第一次月考数学试题上海市控江中学2018-2019学年高三上学期开学考试数学试题北京市东直门中学2019-2020学年高一上学期期中数学试题上海市青浦高级中学2018-2019学年高三上学期9月质量检测数学试题北京市中央民族大学附属中学2018-2019学年高一下学期期末数学试题(已下线)专题01 集合概念与运算-十年(2011-2020)高考真题数学分项(已下线)专题33 算法、复数、推理与证明-十年(2011-2020)高考真题数学分项(七)上海市徐汇区上海中学2020-2021学年高一上学期期中数学试题北京市首都师范大学附属中学2020-2021学年高一下学期期末数学试题(已下线)专题06 集合中的压轴题(2)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)(已下线)1.1 集合的概念与表示-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)上海市建平中学2022届高三上学期9月开学考试数学试题(已下线)模块01 集合与命题-2022年高考数学一轮复习小题多维练(上海专用)北京市昌平区第一中学2021-2022学年高二9月月考数学试题北京市第五十七中学2021-2022学年高二10月月考数学试题上海市行知中学2022届高三上学期10月月考数学试题苏教版(2019) 必修第一册 过关检测 第1章 高考专练 集合北京市第一七一中学2021-2022学年高一下学期期中调研数学试题北京市育才学校2022届高三下学期仿真测试数学试题北京市第五十七中学2022-2023学年高一上学期10月阶段测试数学试题北京市广渠门中学2021-2022学年高二上学期期中数学试题北京十年真题专题01集合北京市陈经纶中学2023-2024学年高二上学期10月月考数学试题(已下线)集合及其运算(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)专题1 集合及其运算(高考真题素材之十年高考)(已下线)1.1 集合及其运算(高考真题素材之十年高考)
2 . 已知集合
,且
中的元素个数
大于等于5.若集合
中存在四个不同的元素
,使得
,则称集合
是“关联的”,并称集合
是集合
的“关联子集”;若集合
不存在“关联子集”,则称集合
是“独立的”.
分别判断集合
和集合
是“关联的”还是“独立的”?若是“关联的”,写出其所有 的关联子集;
已知集合
是“关联的”,且任取集合
,总存在
的关联子集
,使得
.若
,求证:
是等差数列;
集合
是“独立的”,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cdcb0e77b3ae3e701c6b51e15e2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f1c94368c3a41177ff42cfedc0eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e0ad51c5541ec3dcca4a9845f8b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d89801d24aa43f47d6a366aad0571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ccce8225324817b0577551956464f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8021f4f4c253a00360bf8f9425610e1.png)
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2020届北京市海淀区高三上学期期中数学试题(已下线)专题02 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)北京市海淀区2021届高三模拟试题(一)(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题北京市第五十七中学2021-2022学年高二下学期期末考试数学试题北京市第八中学2023届高三上学期12月测试数学试题上海市上海中学2022届高三下学期高考模拟3数学试题北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题
3 . 设n为正整数,集合A=
,
,
,
,
,
.对于集合A中的任意元素
和
,记
.
(Ⅰ)当n=3时,若
,
,求
和
的值;
(Ⅱ)当
时,对于
中的任意两个不同的元素
,
,证明:
.
(Ⅲ)给定不小于2的正整数n,设B是A的子集,且满足:对于B中的任意两个不同元素
,
,
.写出一个集合B,使其元素个数最多,并说明由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18693093ebe22c307bd7a0e7546c583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94b9e69fb1d4a48e9c24b04f86e496e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93fedde9bb8f927c986094275598b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0350c23ae81d21f565637852d6056cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca0a6e55c27d82230a7341c7a9ff90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1a7bce6e7acbd13e268551c7897f4d.png)
(Ⅰ)当n=3时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9ce0575abdf14f4403b3ddc460cafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0addc2213ff0303a589dc71690ba43bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272ba5e58ecd8f3369b5964590d834e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a193c5c4a0476eef3339aafa9bca0e61.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b927eb0becc15f16353f5ca8a36d28c2.png)
(Ⅲ)给定不小于2的正整数n,设B是A的子集,且满足:对于B中的任意两个不同元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02c2e2b26fe4d99dbd55359ca13a82.png)
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7卷引用:2020届北京市密云区高三第二学期第二次阶段性测试数学试题
2020届北京市密云区高三第二学期第二次阶段性测试数学试题(已下线)专题04 集合中的压轴题(二)-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)北京一零一中学2022届高三上学期统考(二)数学试题北京市中关村中学2022届高三下学期开学测试数学试题北京市第五中学2021届高三上学期10月月考数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列北京市延庆区第一中学2024届高三上学期9月月考数学试题
4 . 通常我们把一个以集合作为元素的集合称为族.若以集合
的子集为元素的族
,满足下列三个条件:(1)
和
在
中;(2)
中的有限个元素取交后得到的集合在
中;(3)
中的任意多个元素取并后得到的集合在
中,则称族
为集合
上的一个拓扑.已知全集
为
的非空真子集,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552911fcffb0021a8572e82bfa6648de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb584b83ae783a0ec8a9b4628b7fca3e.png)
A.族![]() ![]() |
B.族![]() ![]() |
C.族![]() ![]() |
D.若族![]() ![]() ![]() ![]() ![]() ![]() |
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5 . 已知有限集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a98a3d1f11a31e9ab1a3dde94c2d58d.png)
,若集合
中任意元素
都满足
,则称该集合
为收敛集合. 对于收敛集合
,定义
变换有如下操作:从
中任取两个元素
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb853c35a7d17396aa032e33505002f0.png)
,由
中除了
、
以外的元素构成的集合记为
,令
,若集合
还是收敛集合,则可继续实施
变换,得到的新集合记作
,…,如此经过
次
变换后得到的新集合记作
.
(1)设
,请写出
的所有可能的结果;
(2)设
是收敛集合,试判断集合
最多可进行几次
变换,最少可进行几次
变换,并说明理由;
(3)设
,对于集合
反复
变换,当最终所得集合
只有一个元素时,求所有的满足条件的集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a98a3d1f11a31e9ab1a3dde94c2d58d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57089a17ec1558dae4a147406b48b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271cd8952c357b35557f9806eb80e75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb853c35a7d17396aa032e33505002f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f71014e1c782a64b8d71f243b6d005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb853c35a7d17396aa032e33505002f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65514add050e1055e45a226692f516b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c50d2ec8a2ea81610aae441e178bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac680b088d60f7963b6002464f49b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4a5b6abfcb7cf393b9edad2c29e441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
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2020-10-23更新
|
1348次组卷
|
8卷引用:上海市建平中学2020-2021学年高一上学期10月月考数学试题
上海市建平中学2020-2021学年高一上学期10月月考数学试题(已下线)专题03 集合中的压轴题(一)-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)上海市南洋模范中学2022-2023学年高一上学期期中数学试题(已下线)第1章 集合与逻辑(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(沪教版2020必修第一册)(已下线)1.3全集与补集 (第2课时)(分层作业)-【上好课】(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列(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)(已下线)期中真题必刷压轴60题(15个考点专练)-【满分全攻略】(人教A版2019必修第一册)
名校
解题方法
6 . 设A是非空实数集,且
.若对于任意的
,都有
,则称集合A具有性质
;若对于任意的
,都有
,则称集合A具有性质
.
(1)写出一个恰含有两个元素且具有性质
的集合A;
(2)若非空实数集A具有性质
,求证:集合A具有性质
;
(3)设全集
,是否存在具有性质
的非空实数集A,使得集合
具有性质
?若存在,写出这样的一个集合A;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72552b86b4558a36aac78c7148d6a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4970b63e04ae03e833bdb95bd52e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出一个恰含有两个元素且具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)若非空实数集A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(3)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8afa6857b5eaf945d14a6e4d7e5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
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2022-11-17更新
|
601次组卷
|
7卷引用:北京市东城区2021-2022学年高二下学期期末统一检测数学试题
北京市东城区2021-2022学年高二下学期期末统一检测数学试题上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)专题01集合与逻辑(15个考点)(1)北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题(已下线)专题1.8 集合与常用逻辑用语全章综合测试卷(提高篇)-举一反三系列(已下线)重难点01集合与常用逻辑用语(9种解题模型与方法)(1)(已下线)专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)
7 . 已知数列
满足:对任意的
,若
,则
,且
,设集合
,集合
中元素最小值记为
,集合
中元素最大值记为
.
(1)对于数列:
,写出集合
及
;
(2)求证:
不可能为18;
(3)求
的最大值以及
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a54cba92061cd4470f7fde4ed5c1edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3936ff665accd1cfd1ff790f9dba518e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69836a99a93afdee1fed09226971a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8fdbba79ddbc156bbb300b1b051e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58e9d04712c58c5d5263ce2dc57e6db.png)
(1)对于数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f014ca9551d95abc843e906e58c60555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b93b1aca2f6d74a84e04eaef8e211b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03884cbb941b58d23a64e6e9e38ab453.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58e9d04712c58c5d5263ce2dc57e6db.png)
您最近一年使用:0次
名校
8 . 设
是不小于3的正整数,集合
,对于集合
中任意两个元素
,
.
定义1:
.
定义2:若
,则称
,
互为相反元素,记作
,或
.
(Ⅰ)若
,
,
,试写出
,
,以及
的值;
(Ⅱ)若
,证明:
;
(Ⅲ)设
是小于
的正奇数,至少含有两个元素的集合
,且对于集合
中任意两个不相同的元素
,
,都有
,试求集合
中元素个数的所有可能值.
![](https://img.xkw.com/dksih/QBM/2019/5/29/2213677049249792/2214678931529728/STEM/fc9eda8df5794756b0651aad13deae50.png?resizew=13)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d9fcf5398bd0f9857193430bdea44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb4290cab93c0521d2596031625448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab4bb60c49a5bc66f40a13fd77fd45c.png)
定义1:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b907e477157421788070fa7b168315.png)
定义2:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa934581daabe793f049138397ef34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb4290cab93c0521d2596031625448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab4bb60c49a5bc66f40a13fd77fd45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601614c932fe6d852fff76488eebcce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab1d8e0b76ed11ddddbc2c14554000b.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e4a92a0731d0eaca247a21a4a2aadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52b1ec97d7091a7d0d267dffff3f7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9297cd87607255b5c2258b00d43c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce7c9333b595345225d8a1925e4d581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4825990d7720b3e88f14deb1e7123ef.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c06cadeefb15a08344b91b954245691.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e83925c979f4f0d3802cdfa37a88c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb4290cab93c0521d2596031625448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab4bb60c49a5bc66f40a13fd77fd45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c81713099c880d5bae5e8bfedc96fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2019-05-30更新
|
1227次组卷
|
3卷引用:【区级联考】北京市房山区2019届高三第二次高考模拟检测数学(理科)试题
【区级联考】北京市房山区2019届高三第二次高考模拟检测数学(理科)试题上海市吴淞中学2019-2020学年高一上学期10月月考数学试题(已下线)专题03 集合中的压轴题(一)-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)
9 . 整数
,集合
,A,B,C是集合P的3个非空子集,记
,为所有满足
,
的有序集合对
的个数.
(1)求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc5735838e43b7a229e8f45c9bfffb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e573725868ff2a04051a268e083f24ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04226e7f36bb2ecb11ffc23c9b7bda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c199451630db4579cde45f8d316765de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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名校
10 . 若集合
,集合
,其中
,则称集合
是集合
的一个“
元子集”.若“
元子集”
中的元素
满足对任意
,恒有
,则称
为
的一个“个性独立子集”.已知集合
,集合
是
的一个“个性独立子集”.
(1)求所有满足条件的集合
的个数;
(2)若
且互不相等,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b7c647eb8e6be44689333e1a6f1f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ed4e9293f5066fe367cfa541afa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d87fa699e2aca137f69e4ac0883dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4aecf0b7edfa826f73389322a52cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c01531dd639f0ad3da0098febbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effaffc8a4d01f865a79933d3c337060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求所有满足条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3fa353ea21d2dea55e32a354e3dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0736f73b81bec1c5d4efe968cfbe2a.png)
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