名校
解题方法
1 . 已知集合
的元素个数为
且元素均为正整数,若能够将集合
分成元素个数相同且两两没有公共元素的三个集合
、
、
,即
,
,
,
,其中
,
,
,且满足
,
,
、
、
、
,则称集合
为“完美集合”.
(1)若集合
,
,判断集合
和集合
是否为“完美集合”?并说明理由;
(2)已知集合
为“完美集合”,求正整数
的值;
(3)设集合
,证明:集合
为“完美集合”的一个必要条件是
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da10a46022dba014432f4b8c9a33a3c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d5add49505a286370d75c05bb37a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29cd450d0feaea9acb27a60430f4a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521c8f3f084af427ec1c464f8b6bed86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7bb58dca886fc65d874e2b30040c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9cfd1398bb75618f8221abd14e97af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5049cefc642e08e2ba05e4f1029486de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ca97c733e72b990f1ce7a39aea6510.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5528d8496504b48fe16e8d4990fc9380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b052876711132da9ca65a3330251bbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bc70fdaa725f9350b5a3356edeeb52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29d686add2ae40bc9001ad85d2ef14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71146e2f4a7ed5efd2585021ecb820f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d1a5cd2d7e140e41954c40198f508b.png)
您最近一年使用:0次
名校
2 . 已知集合
和
,使得
,
,并且
的元素乘积等于
的元素和,写出所有满足条件的集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960e519ffa04e906697895f1b48686cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521c8f3f084af427ec1c464f8b6bed86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
您最近一年使用:0次
2021-10-21更新
|
1464次组卷
|
16卷引用:专题1-1 集合及集合思想应用(讲+练)-3
(已下线)专题1-1 集合及集合思想应用(讲+练)-3上海市普陀区桃浦中学2021-2022学年高一上学期10月月考数学试题上海市徐汇区位育中学2021-2022学年高一上学期期中数学试题(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)1.1 集合的运算(第4课时)(已下线)上海高一上学期期中【压轴42题专练】(1)(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)高一上学期期中【压轴60题考点专练】(必修一前三章)-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【易错60题考点专练】(必修一前三章)-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)高一上学期第一次月考填空题压轴题50题专练-举一反三系列安徽省桐城中学2023-2024学年高一上学期9月月考数学试题上海市位育中学2023-2024学年高一上学期10月月考数学试题(已下线)第一章 集合与逻辑(单元提升卷)-【满分全攻略】(沪教版2020必修第一册)(已下线)上海市高一上学期【第一次月考卷】-【满分全攻略】(沪教版2020必修第一册)(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)期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)
名校
3 . 已知数集
.若存在
,使得对任意
都有
,则称A为完美集,给出下列四个结论:
①存在
,使得
为完美集;
②存在
,使得
为完美集;
③如果
,那么
一定不为完美集;
④使得A为完美集的所有
的值之和为-2.
其中,所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ec6f9bc15b17f9bc16c32310d12af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc64bec6275d06d9d37e12062fa68e27.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee2a932505404134b5c9cc985e6619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881e868548a7c781a2a1083134ce9971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
③如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7277da79d5ea922cfa0e16c6faebe7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
④使得A为完美集的所有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
其中,所有正确结论的序号是
您最近一年使用:0次
2021-10-11更新
|
1333次组卷
|
7卷引用:北京市海淀区中国人民大学附属中学2022届高三10月月考数学试题
北京市海淀区中国人民大学附属中学2022届高三10月月考数学试题(已下线)热点02 集合与常用逻辑用语-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)专题01 集合-2(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(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)高一上学期期中考试填空题压轴题50题专练-举一反三系列(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
4 . 设数集
满足:①任意
,有
;②任意
、
,有
或
,则称数集
具有性质
.
(1)判断数集
是否具有性质
,并说明理由;
(2)若数集
且
具有性质
.
(i)当
时,求证:
、
、
、
是等差数列;
(ii)当
、
、
、
不是等差数列时,写出
的最大值.(结论不需要证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8647b00cc8c8f35555c7d78cf2812c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c8b2714e2f6ddfdd6b05d3b4de1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8e5872f45d4b878b0119997cb5bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84734fbba70c0b45045fabf8090f810b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2161a642b95463642adc3892850bc74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddc189d2c675b0e2ade4f7ed40f66fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8509c4b8fef1e10a20fe1c3e9243ac8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c7867969b14fd642147188b6ebf29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-09-26更新
|
589次组卷
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7卷引用:北京市丰台区2021届高三二模数学试题
5 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46d91a898eabc0094137dacb4defa60.png)
.对于
,
,定义
,定义
与
之间的距离为
.
(1)设
,
,
,直接写出
,
,
;
(2)
,判断
与
的大小关系,并给出证明;
(3)证明:
,
,
,
三个数中至少有一个是偶数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46d91a898eabc0094137dacb4defa60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a213c770b7898200a9f0fd3f48e7403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aea343234102eeccd40f790ec5ce2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374c2acfb112a4284400b5ddbd19aa02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a0b3823a1fd3e69af7594da9b8f0f0.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/a005c90b3e44a1737dd3771dbafcb5c2.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5794bdc5eb3d74aedd9c05d6de2d69c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea406d4bc7d7fb5d6f0789441028f21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207ff0926bf917ce30f615d23eff451c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507d7d4b676e2b1cd0b2bec2fffda025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7041adbdd3371e7cd4bd02682115ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519a1fbbf2ae4158090a505c9494b0e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858291a961c75db554dc5a737c1fcd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519a1fbbf2ae4158090a505c9494b0e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6e825795c828f8281e93607d0e1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdfd65ee99c3d93adee6732ae125eb8.png)
您最近一年使用:0次
名校
6 . 对于平面上的两个点
,
,若满足①
,②
,③前面两个不等式中至少有一个“
”不成立,则称
是相对于
的一个优先点,记作“
”. 已知点集
.
(Ⅰ)若
,
,则可以构成_____ 组优先点;
(Ⅱ)若点集
,且集合
中的任意两个点都不能构成一组优先点,则集合
中的元素最多可以有_____ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f1553650bd8990580c75bd7698256f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2315ad24dac85ab6a18b2b6f654726b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc24c4a930bca9ae9b2f3746e48e644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f8f97cf2fc2d0676d6df01ff9759611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5b2a1b766ec0f01ae5fc7ea384899a.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04b8b04cf8ca5049bcc495e512c667c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
(Ⅱ)若点集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60045585a73813c6c28ab7a0f4fd266e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
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2021-09-25更新
|
412次组卷
|
2卷引用:北京市第十三中学2022届高三上学期开学考数学试题
7 . 已知集合M={x∈N|1≤x≤21},集合A1,A2,A3满足①每个集合都恰有7个元素; ②A1∪A2∪A3=M.集合Ai中元素的最大值与最小值之和称为集合Ai的特征数,记为Xi(i=1,2,3),则X1+X2+X3的最大值与最小值的和为___ .
您最近一年使用:0次
2021-09-19更新
|
1208次组卷
|
11卷引用:【区级联考】北京延庆区2019届高三一模数学(理)试题
【区级联考】北京延庆区2019届高三一模数学(理)试题(已下线)专题1.1 集合-(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题01 集合-2022年高考数学一轮复习小题多维练(新高考版)(已下线)专题8.3 临界知识问题 玩转压轴题-玩转压轴题,进军满分之2021高考数学选择题填空题(已下线)第01节 集合(好题帮)(已下线)专题1-1 集合及集合思想应用(讲+练)-3福建省泉州科技中学2021-2022学年高一上学期第一次月考数学试题(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(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)高一上学期期中考试填空题压轴题50题专练-举一反三系列湖南省长沙市明德中学2023-2024学年高二下学期3月阶段测试数学试卷
8 . 集合
,
,
都是非空集合,现规定如下运算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9f61c3ea47db2af36e081b22f0a079.png)
且
.假设集合
,
,
,其中实数
,
,
,
,
,
满足:(1)
,
;
;(2)
;(3)
.计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ec8db729c8b2af58bed3d02545629f.png)
____________________________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9f61c3ea47db2af36e081b22f0a079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12889e298e054786bb6042a862617c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f1cbf2cc8097db652706f2222f2387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4cf73e77e7f40c53e4003b5e07ac030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cb80b0fe505128f6405469b08e9280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79a8f2aa08be6e17d3e1d482213a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee27e3c1e6527402e182110e3099afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e191682fbeb1b82d9fe4bc319ab0a75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387c917662e5ebe82ec94cc94132b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0cfe0f1c59cf33464d623a9da49b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ec8db729c8b2af58bed3d02545629f.png)
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20卷引用:2015年山东省春季高考数学真题
2015年山东省春季高考数学真题(已下线)热点02 集合与常用逻辑用语-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)技巧02 填空题解法与技巧(练)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)查补易混易错点01 集合与常用逻辑用语-【查漏补缺】2022年高考数学(理)三轮冲刺过关(已下线)2022年高考考前20天终极冲刺攻略(四)【理科数学】(6月5日)(已下线)考点3 与集合相关的新定义问题 --2024届高考数学考点总动员【练】(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)第1章 集合 单元综合检测(难点)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)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填空题压轴题50题专练-举一反三系列上海市曹杨第二中学2023-2024学年高一上学期第一次月考(10月)数学试题(已下线)难关必刷01集合的综合问题(3种题型30题专项训练)-【满分全攻略】(沪教版2020必修第一册)(已下线)期中模拟卷(上海专用)-【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)期中真题必刷易错60题(26个考点专练)-【满分全攻略】(人教A版2019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)(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(已下线)第1章 集合与常用逻辑用语-【优化数学】单元测试基础卷(人教B版2019)
9 . 给定正整数
,集合
,若存在集合A,B,C,同时满足下列条件:①
,且
;②集合A中的元素都为奇数,集合B中的元素都为偶数,所有能被3整除的数都在集合C中
集合C中还可以包含其他数
;③集合A,B,C中各元素之和分别记为
,
,
,有
,则称集合
为可分集合.
(1)已知
为可分集合,写出一组满足条件的集合A,B,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471a6f260c478862141ca5fcf654e05e.png)
(2)求证:若n是3的倍数,则
不是可分集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a140d6d30530e4f67c8325308d476.png)
(3)若
为可分集合且n为奇数,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac724d00ff62af81aa435c87817de866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed712132fb66567e4e806eaf21af7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459af7df9f13eafa5f85c85f996c647f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea3c7cd2f23b4521e64a7e64844ec48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e8a7f6c535fc3cd270af428d55f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2361c60ae76195982a221de8a380b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadf7483681e66386d3a4cc2a6f818b.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadf7483681e66386d3a4cc2a6f818b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471a6f260c478862141ca5fcf654e05e.png)
(2)求证:若n是3的倍数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadf7483681e66386d3a4cc2a6f818b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a140d6d30530e4f67c8325308d476.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadf7483681e66386d3a4cc2a6f818b.png)
您最近一年使用:0次
2021-08-29更新
|
382次组卷
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3卷引用:北京市北京交通大学附属中学2022届高三上学期开学考试数学试题
北京市北京交通大学附属中学2022届高三上学期开学考试数学试题北京市第一七一中学2023届高三上学期期中数学质量检测试题(已下线)1.3 交集、并集-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)
10 . 对于有限个自然数组成的集合
,定义集合
,记集合
的元素个数为
.定义变换
,变换
将集合
变换为集合
.
(1)若
,求
;
(2)若集合
,证明:
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69154dbf052ecb6866028801051aa0e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0928441297e887330350a46dd2b40841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4f30fe128cb72f71b144937e4093d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b403fc36865ed11b00995a8321e52b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928a2f491d5b6e5acb87888663aec0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344d95d02bc0b476768fabe18105289b.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8f14b19f026b10473b3377b3fbf342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811a0f2a63600129f7143128884dd144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2216940861922a85b6a947a4317ef753.png)
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7卷引用:专题02命题与常用逻辑-2022年新高三数学暑假自学课精讲精练
专题02命题与常用逻辑-2022年新高三数学暑假自学课精讲精练安徽省合肥市第一中学2020-2021学年高一上学期第一次段考数学试题(已下线)1.2 充分条件与必要条件提高练-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)2.2 充分条件、必要条件、充要条件湖南师范大学附属中学2022-2023学年高一上学期第一次大练习数学试题北京市第八十中学2022-2023学年高一上学期九月月考数学试题(已下线)专题01 集合与常用逻辑用语4-寒假作业单元合订本