1 . 在
)个实数组成的n行n列的数表中,
表示第i行第j列的数,记
,
若
∈
,且
两两不等,则称此表为“n阶H表”,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
且
,求证:
为偶数;
(3)求证:不存在“5阶H表”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff6f8857124f7bbc5a1c65c2e83767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9ff2b00c2841318b2697b070201a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2fe368efe94c1e98309473e49a92fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d253e22a1d9709dca48c6e0c649b47bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0fdc4f349ea9634160ce08ac269691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db8c7f00e535ec1ffbb7008711b2096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8810a8ced3ca8dae09180a663275b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求证:不存在“5阶H表”.
您最近一年使用:0次
2023-03-14更新
|
872次组卷
|
5卷引用:专题1 集合新定义题(九省联考第19题模式)练
(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)微考点8-1 新高考新题型19题新定义题型精选北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题北京市第一0一中学2023届高三数学统练三试题北京市第十一中学2023届高三三模(5月)数学试题
名校
2 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
573次组卷
|
5卷引用:专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本北京市顺义区2022-2023学年高一下学期期末质量监测数学试题重庆市南开中学校2023-2024学年高一上学期开学考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)
3 . 已知集合
.若对于集合M的任意k元子集A,A中必有4个元素的和为
,则称这样的正整数k为“好数”,所有“好数”的最小值记作
.
(1)当
,即集合
.
(i)写出M的一个子集B,且B中存在4个元素的和为
;
(ii)写出M的一个5元子集C,使得C中任意4个元素的和大于
;
(2)证明:
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fcb12b12b124d437768cfc9bc3a23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e48acb84d3c7fb67ed275add00ea178.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72790d6daf2b07dfbbbc7a340eeb6ffb.png)
(i)写出M的一个子集B,且B中存在4个元素的和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(ii)写出M的一个5元子集C,使得C中任意4个元素的和大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c5470cb4bb49c443a9568d79eadd39.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831fa5ef5f6cea7664a4d385b7c98105.png)
您最近一年使用:0次
2023-04-06更新
|
920次组卷
|
6卷引用:专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)
(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大题型)(练习)北京市门头沟区2023届高三综合练习(一)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)
名校
4 . 已知集合
,规定:若集合
,则称
为集合
的一个分拆,当且仅当:
,
,…,
时,
与
为同一分拆,所有不同的分拆种数记为
.例如:当
,
时,集合
的所有分拆为:
,
,
,即
.
(1)求
;
(2)试用
、
表示
;
(3)设
,规定
,证明:当
时,
与
同为奇数或者同为偶数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb813e225b094c636d38d0e0cfbd67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea40e6c6055a63e7934f614e878940ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c3c3b06e4d829c5967bd76ab3d14ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ff4c4d26a22d8ab9e6a70cadf6623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28faa23f36fcfc2aef9cc68f46b1c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdc216147253ff9697788764dc1ab93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a871a43ca9e77e26f5c6b680c165e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b704d8979f50009bcb3ec36a07864d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1fdd193767192adc5adcd772ae2b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da1c8d2d0ddab6eed4da334b0446849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a045201f479d99c868e5bac5632b211.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe036f3bc2712beea23557116fdac74c.png)
(2)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9acc25eced79e4d6973d2edeb5628c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ba78808895f5e4bd393fe7aa5b9a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bb215f28e5eea7ff4c7ca5ee9e2216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-07更新
|
1144次组卷
|
8卷引用:第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)单元测试B卷——第六章 计数原理上海市实验学校2022-2023学年高二上学期期末数学试题(已下线)6.5二项式定理(分层练习)-2022-2023学年高二数学同步精品课堂(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(基础、常考、易错、压轴)分类专项训练-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)(已下线)期中考试押题卷(考试范围:第6-7章)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)
解题方法
5 . 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
|
903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
6 . 已知集合
是集合
的子集,对于
,定义
.任取
的两个不同子集
,
,对任意
.
(1)判断
是否正确?并说明理由;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d39a39a70dacd0402f6fdd59a0e879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc718cf6749da06b2dd90e9b2751854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1171081d25910d6bb0bf9d32e82e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d39a39a70dacd0402f6fdd59a0e879.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/0fc718cf6749da06b2dd90e9b2751854.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ac3d72ad811d426884f100f32aa0a2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4090eff6726fa4e3a32655b3fba41abe.png)
您最近一年使用:0次
名校
7 . 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
|
1998次组卷
|
13卷引用:高三数学临考冲刺原创卷(二)
(已下线)高三数学临考冲刺原创卷(二)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)(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)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(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
名校
8 . 设集合
,集合
,如果对于任意元素
,都有
或
,则称集合
为
的自邻集.记
为集合
的所有自邻集中最大元素为
的集合的个数.
(1)直接判断集合
和
是否为
的自邻集;
(2)比较
和
的大小,并说明理由;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8d9e00ef22cd220a6bbd291f280a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cd2449f6ae27a72287be95a661d8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320a7c616f6f7207a0a38bb707ac2205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbcd3d6b77c949be81a946ac9ed9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73707750f88b56101446fce394e0faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7f71b0119f257edb8d5060a810de92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)直接判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4047b80385ef60ea5e9a1f184e7b948b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecde0085a473948c061942a1728a37c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64927a98d33b49dc5c6a0e65e5e8eb53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41788e238eff245e567b58dea3a0003.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293bd318a7a3796d3589db25148be688.png)
您最近一年使用:0次
名校
解题方法
9 . 设
为非空集合,定义
(其中
表示有序对),称
的任意非空子集
为
上的一个关系.例如
时,
与
都是
上的关系.设
为非空集合
上的关系.给出如下定义:①(自反性)若对任意
,有
,则称
在
上是自反的;②(对称性)若对任意
,有
,则称
在
上是对称的;③(传递性)若对任意
,有
,则称
在
上是传递的.如果
上关系
同时满足上述3条性质,则称
为
上的等价关系.任给集合
,定义
为
.
(1)若
,问:
上关系有多少个?
上等价关系有多少个?(不必说明理由)
(2)若集合
有
个元素
,
的非空子集
两两交集为空集,且
,求证:
为
上的等价关系.
(3)若集合
有
个元素
,问:对
上的任意等价关系
,是否存在
的非空子集
,其中任意两个交集为空集,且
,使得
?请判断并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5993d7b820c0b182711674de0d85a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978ef4aebb02ab0320e8ff61d7195392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba8172b545998849067b299ac4949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddf512fd22bcd30c39da2a8ef41a82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd8717bdcfbc527676ae2a80285881e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7d20713240ffa343a7b7b8da43c577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532da63ac3aa945328904b9db8b05bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928008f619c199d9375b03b63f17f0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248bff56f76fc98ac9e16b2c751bc142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/256b72e8048ad33ee1f6919b04b70ab7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若集合
![](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/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.png)
您最近一年使用:0次
10 . 若集合
(
)满足:对任意
(
),均存在
(
),使得
,则称
具有性质
.
(1)判断集合
,
是否具有性质
;(只需写出结论)
(2)已知集合
(
)具有性质
.
(
)求
;
(
)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308975da991b918217d1ee03ad1830ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09737e117adb481fd3c4affdf38ff45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0a9f2d0e6e1c56d862a178f1d4a1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7bf76d1e4ec87759a61a5fda954515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735cf07db1fd80a115aa5fb5213289ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee42f4c9aa90c833e0c9e3d997c7c732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308975da991b918217d1ee03ad1830ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ab6567c156fee308640828a804415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3d8d73a7dea024f7e07a3b6985dcb2.png)
您最近一年使用:0次
2022-01-24更新
|
546次组卷
|
5卷引用:专题01 集合与常用逻辑用语3-寒假作业单元合订本
(已下线)专题01 集合与常用逻辑用语3-寒假作业单元合订本北京市门头沟区2022届高三上学期期末调研数学试题北京市第十四中学2022-2023学年高二下学期期中测试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列北京市广渠门中学2022-2023学年高二上学期9月月考数学试卷