名校
1 . 已知X为包含v个元素的集合(
,
).设A为由X的一些三元子集(含有三个元素的子集)组成的集合,使得X中的任意两个不同的元素,都恰好同时包含在唯一的一个三元子集中,则称
组成一个v阶的Steiner三元系.若
为一个7阶的Steiner三元系,则集合A中元素的个数为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0953f915a38732687056d9e2dee04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6ce9503fa100664e4aa127f513a167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8721733e3975550483a89a78203dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8721733e3975550483a89a78203dd.png)
您最近一年使用:0次
2023-04-19更新
|
3237次组卷
|
10卷引用:湖北省2023届高三下学期四月调研考试数学试题
湖北省2023届高三下学期四月调研考试数学试题专题01集合与常用逻辑用语(已下线)第01讲 集合(七大题型)(讲义)江苏省南通市新高考2024届高三适应性测试数学模拟试题(已下线)集合及其运算(已下线)新题型01 新高考新结构二十一大考点汇总-1河南省信阳市新县高级中学2024届高三考前第三次适应性考试数学试题(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列(已下线)高一上学期期末考试填空题压轴题50题专练-举一反三系列湖北省武汉市第十一中学2023-2024学年高二下学期6月考数学试题
名校
2 . 给定正整数
,设集合
.对于集合
中的任意元素
和
,记
.设
,且集合
,对于
中任意元素
,若
则称
具有性质
.
(1)判断集合
是否具有性质
?说明理由;
(2)判断是否存在具有性质
的集合
,并加以证明;
(3)若集合
具有性质
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a839578f0b23c8aeba01730563a643e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da8a33568ded09f3450bb153b0e5697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714ab9e5a6949c90c9bfdd118cfabeb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35e477c52dfbfb80f1fc315143c8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368a045ba80f97383f3d9d7fcdc8f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd94234d029d89c7b788b6d1e225db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9855cb665c7f3785a17718be10538af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2f08194bb663f1a086fa2f555ebf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa6d3ee76dcca88508ec0921f1adf0f.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd6650ab1ac1f7426ec68c729671c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c581b105a7e14eae97d650ae73adf710.png)
(2)判断是否存在具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a742b9bb0812b7bb895851cc5a06fa1a.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/faa6d3ee76dcca88508ec0921f1adf0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b74258d0a66cadc32ba68697abca894.png)
您最近一年使用:0次
2023-03-27更新
|
1988次组卷
|
13卷引用:北京市西城区2023届高三一模数学试题
北京市西城区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题01集合与常用逻辑(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21北京卷专题02集合(解答题)北京市海淀区首都师范大学附属中学2024届高三上学期10月阶段检测数学试题(已下线)广东省深圳中学2023-2024学年高三寒假开学适用性考试数学试题(已下线)高三数学临考冲刺原创卷(二)北京市人大附中2022-2023学年高一下学期期中模拟数学试题(已下线)北京市第四中学2022~2023学年高一下学期期中数学试题(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)专题03集合的运算-【倍速学习法】(人教A版2019必修第一册)北京市中关村中学2023-2024学年高二上学期期中练习数学试题
名校
解题方法
3 . 定义两个点集S、T之间的距离集为
,其中
表示两点P、Q之间的距离,已知k、
,
,
,若
,则t的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc583b7bb3ab41850a8a2447a7abaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7033cdfb9fb5770ca833f2c83ecb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450f84739e8a2d21b374ccedc8972605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56d22586bc5fb71fe1b442ee7580268.png)
您最近一年使用:0次
2023-03-02更新
|
2202次组卷
|
9卷引用:上海市嘉定区2023届高三下学期2月调研数学试题
解题方法
4 . 设全集
,集合A是U的真子集.设正整数
,若集合A满足如下三个性质,则称A为U的
子集:
①
;
②
,若
,则
;
③
,若
,则
.
(1)当
时,判断
是否为U的
子集,说明理由;
(2)当
时,若A为U的
子集,求证:
;
(3)当
时,若A为U的
子集,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fefd9d7303a04708b4f2d728e78361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed0c7122ffdbf145d72a310671465fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0412e8d25fa4748e3f6784611bd61990.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8a1b0b32229f6a9f5b85c11f05bee2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658f2824532e5b72962fe34a22c27c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251a5b0faec4a29eff8173a633c0b765.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8489b7692d3889aede2335c3ac8aca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb76e516509e33dc0d29663cc6b884bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd131b82e404452880d7a97792f22493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7844925f9077aa32c990fc20a51467.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcd23a8020d731bd512bb8df45ea594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e13bbde03ffad05ecc3fee8120b6a6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575c2057865186fb80a50f67ee6ea70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
您最近一年使用:0次
2023-01-06更新
|
897次组卷
|
10卷引用:FHsx1225yl138
(已下线)FHsx1225yl138北京市朝阳区2022-2023学年高一上学期数学期末试题北京市第五十七中学2022-2023学年高一(1+3科技创新试验班)下学期期中考试数学试题(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(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(已下线)专题03集合的运算-【倍速学习法】(人教A版2019必修第一册)(已下线)第一章 集合与常用逻辑用语(单元提升卷)-【满分全攻略】(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)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
5 . 设
、
、
、
、
是均含有
个元素的集合,且
,
,记
,则
中元素个数的最小值是( )
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b832048aa929fbb3542f1ccfccb6fe19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bdfbeb9e4e56f2d8fcf4547c599cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3040ca4961213b15ef00b151cf0c83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a8398fd769872cabf1d4835180aff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-12-15更新
|
2401次组卷
|
13卷引用:上海市普陀区2023届高考一模数学试题
上海市普陀区2023届高考一模数学试题重庆市缙云教育联盟2023届高三二模数学试题(已下线)模块六 专题8 易错题目重组卷(重庆卷)湖北省部分名校2023届高三二模数学试题(已下线)集合及其运算河北省邯郸市魏县2022-2023学年高一上学期期末考试数学试题(已下线)第1章 集合与常用逻辑用语(单元测试卷)-【上好课】(已下线)高一上学期第一次月考选择题压轴题50题专练-举一反三系列上海市南汇中学2023-2024学年高一上学期10月月考数学试题(已下线)专题1-2 集合运算求参与最值10种题型归类(2) - -【巅峰课堂】题型归纳与培优练(已下线)第一章 集合与常用逻辑用语(压轴题专练)-速记·巧练(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)(已下线)高一上学期期末考试选择题压轴题50题专练-举一反三系列
名校
6 . 设集合M是实数集
的子集,如果
满足:对任意
,都存在
,使得
,则称t为集合M的聚点,则在下列集合中,以0为聚点的集合有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cf951919b39035bcf7f59fc513b549.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-09-25更新
|
269次组卷
|
7卷引用:重庆市2024届高三上学期11月月度质量检测数学试题
重庆市2024届高三上学期11月月度质量检测数学试题重庆市第一中学2021-2022学年高一上学期10月月考数学试题四川省内江市资中县第二中学2022-2023学年高一上学期10月月考数学试题江苏省南京市中华中学2023-2024学年高一上学期学情调研(一)数学试题江苏省连云港市海滨中学2023-2024学年高一上学期第一次月考数学试题(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)专题01 集合及其运算2-【寒假自学课】(苏教版2019)
7 . 已知定义在
上的函数
(
是自然对数的底数)满足
,且
,删除无穷数列
、
、
、
、
、
中的第
项、第
项、
、第
项、
、
,余下的项按原来顺序组成一个新数列
,记数列
前
项和为
.
(1)求函数
的解析式;
(2)已知数列
的通项公式是
,
,
,求函数
的解析式;
(3)设集合
是实数集
的非空子集,如果正实数
满足:对任意
、
,都有
,设称
为集合
的一个“阈度”;记集合
,试问集合
存在“阈度”吗?若存在,求出集合
“阈度”的取值范围;若不存在,请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fee69eaf31dfeb48c691c12384f2d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35679c97cf16aa592343787a756c7c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8c7bb4fe82c62be38565dae4d303b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6db29ed83804b2f681b09cc1b468c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93205440edb7ad3fe4f13ea76dd29b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2470c8ff34402484c137086752eb5e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54289962af94fdf6270d10e3123ccb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdbc09b10e4b1a63db906f15469c139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
名校
解题方法
8 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若
为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377240e8ad277805e0499803d5be5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623eef12f37f0b85ddd367faa9b3bfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
您最近一年使用:0次
2023-05-28更新
|
708次组卷
|
11卷引用:北京市西城区2021届高三5月二模数学试题
北京市西城区2021届高三5月二模数学试题北京一零一中学2023届高三下学期数学统练四试题北京卷专题02集合(解答题)北京市第一0一中学2022-2023学年高三下学期统练数学试卷(四)北京市东城区景山学校2024届高三上学期12月月考数学试题(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)北京市第五十七中学2021-2022学年高二上学期期中检测数学试题北京市第二十中学2022-2023学年高二上学期12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北京师范大学第二附属中学2023-2024学年高二上学期期中测试数学试题北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷
9 . 已知数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
,
为从1到2022互不相同的整数的一个排列,设集合
,
中元素的最大值记为
,最小值记为
.
(1)若
为:1,3,5,…,2019,2021,2022,2020,2018,…,4,2,且
,写出
,
的值;
(2)若
,求
的最大值及
最小值;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f1e6715f78f92638d566e1806ca516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3e9ef023f9cb43f9c9930f3b9620a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9477141f053e191d0a38e2e5dedf944.png)
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef178c4320412a41a6592d5e0a833bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef178c4320412a41a6592d5e0a833bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a05744bb22c9562706b334e9e1e889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
10 . 设集合
,
,
,
中至少有两个元素,且
满足:①对于任意
,若
,都有
;②对于任意
,若
,则
;
(1)判断下列两组集合是否满足要求:
(ⅰ)若
,则
;
(ⅱ)若
,则
;
(2)证明:若
有
个元素,则
有
个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef9096420672673840303a14f0fb636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6f228e37ac7282f2f013eda7395683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8339eab9c659e50db86828b65f825e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566d386cbedb1c8750f4837633c2af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5718e9c8baa106b447f9fae23e730de.png)
(1)判断下列两组集合是否满足要求:
(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e1540256cea69dcfb735c3e03eccdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04d7b603e86497db23bc2b124a8e5c.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dbc6c0414c93f1dd3e4945bd34d082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76bd82972fa678045162f19fee8142f.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af500a4e28d6f5b38390b7642eb96ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
您最近一年使用:0次