名校
1 . 已知集合
为非空数集,定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d137957c0cf9c5f99bd883fe20a0b945.png)
(1)若集合
,请直接写出集合
:
(2)若集合
,且
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d137957c0cf9c5f99bd883fe20a0b945.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8d171c3d2d86dc5594cffb51096fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76ad1e03a6ba59e8164e37c5e7e063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
您最近一年使用:0次
解题方法
2 . 已知集合
,
,其中
,且
.若
,且对集合A中的任意两个元素
,都有
,则称集合A具有性质P.
(1)判断集合
是否具有性质P;并另外写出一个具有性质P且含5个元素的集合A;
(2)若集合
具有性质P.
①求证:
的最大值不小于
;
②求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9a3f4c7334a730ea37d803402891d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8b572950af972d5e265f689e35314c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368a045ba80f97383f3d9d7fcdc8f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a0838190df3e2d7328dae29243d10a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85463b225751e4fb81ae802db61176bb.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6632f39a4c514336a74d274bb3d6a77d.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8b572950af972d5e265f689e35314c.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2b789cb4ce6b7919d64d88dbdc1c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7426bc7343f7c515f079530f93e0c3a.png)
②求n的最大值.
您最近一年使用:0次
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
|
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
|
1251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
6 . 设
是一个非空集合,由
的一切子集(包括
,
自身)为元素构成的集合,称为
的幂集,记为
.
(1)当
时,写出
;
(2)证明:对任意集合
,都满足
;
(3)设
是
个两位数字形成的集合,证明:
中必有两个
的子集,其元素的数值和相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1677491ba90508b0e815b566447a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7549990c248033f634d6b243b1b2dfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
(2)证明:对任意集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6fcd46d3cf19bb064958759ff2b3a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580756dffbc89ae37acef0f48d5c1140.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e044325ad7fdaef36758daa8b9fe4456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c4b9c60fdb001f63be75985dce0615.png)
您最近一年使用:0次
2022-10-21更新
|
147次组卷
|
2卷引用:河南省周口市川汇区周口恒大中学2023-2024学年高一上学期期中数学试题
名校
7 . 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
|
1443次组卷
|
10卷引用: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
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(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)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(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)
8 . 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)
您最近一年使用:0次
2022-04-09更新
|
755次组卷
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5卷引用:1.3 交集、并集(2)
(已下线)1.3 交集、并集(2)(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)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)
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9 . 对正整数
,记
,
.
(1)用列举法表示集合
;
(2)求集合
中元素的个数;
(3)若
的子集
中任意两个元素的和不是整数的平方,则称
为“稀疏集”,证明:存在
使得
能分成两个不相交的稀疏集的并集,且
的最大值为14.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a1b26aa2a8eae39c45ab0b5e4b0888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d38f7005b0c6ade2daf8bf39c17c957.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e24e843f778f53af4f3c9e25faa809.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-10-13更新
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180次组卷
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4卷引用:第一章 集合与逻辑(单元基础卷)-【满分全攻略】(沪教版2020必修第一册)
(已下线)第一章 集合与逻辑(单元基础卷)-【满分全攻略】(沪教版2020必修第一册)(已下线)专题01集合及其表示方法2-【倍速学习法】(沪教版2020必修第一册)上海市华东师范大学第三附属中学2022-2023学年高一上学期第一次阶段检测(10月)数学试题上海市浦东新区新川中学2022-2023学年高一上学期期中数学试题
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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