1 . 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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2021-08-28更新
|
1090次组卷
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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
名校
2 . 已知集合
,若
且
,则称
为集合生成的一个“交错数”,所有“交错数”组成的集合
称为集合
生成的交错集
(1)写出集合
生成的交错集;
(2)若集合
,求证:集合
的交错数各不相同;
(3)无穷数列
的前
项和为
,且对任意
都有
.记
,判断集合
生成的交错集
与正整数集
的关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd2491dc0189bacbcb09d74ee95e9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8bb74bfdabb77c25312c1636fcf309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73df366305c13505aa32d142f8e96e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53a5ea9c349d77bdd3e19dfdcaa6784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604f15dc563da9528ee12d1b2bb341e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5bc58791e16a37f58c66d95e905ad4.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdff394b957c5d6881d041a887758d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ddd6d99ad32dd7fdb1797d8cf94786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66e3cd1e23a2ee92c01c030642d8df4.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/52866a74e4af867ceea0efb1ad06602c.png)
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3 . 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)
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2021高三·全国·专题练习
名校
4 . 已知集合
为非空数集,定义
,
.
(1)若集合
,直接写出集合
及
;
(2)若集合
,
,且
,求证
;
(3)若集
,且
,求集合
中元素的个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f43ef1d76f7a33e2aaa5c0f63f53b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ad3621cf61323c074b8b9f075fb65f.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e002c65f15d75af50420ac6173348ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7591668ec1bc5e8b1f2c4dba4835d1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3cd4e59bf251858f03408b59ad1902.png)
(3)若集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3fe454c4e4cefbc55828f34088558a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4d331fa6921e8ebc0b1fc4affd22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2021-03-20更新
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941次组卷
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4卷引用:专题01 集合与常用逻辑用语-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)
(已下线)专题01 集合与常用逻辑用语-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)(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)北京市清华大学附属中学2019-2020学年高一上学期期末数学试题四川省泸州市泸县泸县第四中学2023-2024学年高一上学期10月月考数学试题
5 . 设数列
.定义集合
,
,其中
为给的正整数.
(1)若
,求
;
(2)若
中的项
,求证:
为常数列;
(3)记集合
的最大元素为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cef122118d272825a7bc8c336f1bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f4ab40307da20dd6a011ef33c51b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b8909e1435bc70e6f209b2df94de88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd8aecb16302a7973a6d4eb86c3cc6e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd2c56d022774693603879f37b5dc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1435ac5c72edbdf99c02c6354870e4d3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49571ac4685f51e68bab0b282dbd0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd62c987ebd28ec20e8d59d1a3b02c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520a8a20577ce2f7aa9533516b80dead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970aca8f11113fa58bc11998a5ed0b1b.png)
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名校
6 . 已知集合
为非空数集,定义:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092a46bd0eb089045217e1b13ccbb65.png)
(1)若集合
,直接写出集合
,
.
(2)若集合
,
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
,
,
,记
为集合
中元素的个数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0d6adf2d45f344e1ca24c4cf0e4884c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e092a46bd0eb089045217e1b13ccbb65.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa9c26b45f6947550f7c40cbfdecbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faaa2c9b8bc8ee534a517d6a108a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76ad1e03a6ba59e8164e37c5e7e063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b408aeda05ba8f05babea6251dcab2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650aa72fd4034517f9f981e382c1e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650aa72fd4034517f9f981e382c1e50.png)
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2020-11-15更新
|
2487次组卷
|
21卷引用:专题01 集合与逻辑(讲义)-2
(已下线)专题01 集合与逻辑(讲义)-2(已下线)集合及其运算湖南省长沙市湖南师大附中2020-2021学年高一上学期第一次大练习数学试题北京大学附属中学2020-2021学年度高一10月考衔接班数学A层试题北京市海淀区中国人民大学附属中学2020-2021学年高一(上)期中数学试题北京市中国人民大学附属中学2020-2021学年度高一年级上学期数学期中练习试题北京人大附中2020-2021学年高一(上)期中数学试题(已下线)期末测试(能力提升)(1)-2020-2021学年高一数学(必修一)单元测试定心卷(沪教版2020)(已下线)高一上学期期末全真模拟02-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)(已下线)知识点03 交集、并集-2021-2022学年高一数学同步精品课堂讲+例+测(苏教版2019必修第一册)(已下线)第3课时 课后 集合的基本运算(已下线)第一单元 (基础过关)集合与常用逻辑用语 A卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)(已下线)第03讲 交集、并集(教师版)-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第一册)第1章 集合(章末测试提高卷)-2021-2022学年高一数学同步单元测试定心卷(苏教版2019必修第一册)(已下线)专题03 集合的运算压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)北京市广渠门中学2021-2022学年高一上学期期中质量检测数学试题(已下线)1.3 交集、并集第一章 预备知识 期末综合复习测评卷-2021-2022学年高一上学期数学北师大版(2019)必修第一册(已下线)第3课时 课后 交集、并集(完成)(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)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)
解题方法
7 . 对给定的正整数
,令
,
,
,
,
,
,2,3,
,
.对任意的
,
,
,
,
,
,
,
,定义
与
的距离
.设
是
的含有至少两个元素的子集,集合
,
,
中的最小值称为
的特征,记作
(A).
(Ⅰ)当
时,直接写出下述集合的特征:
,0,
,
,1,
,
,0,
,
,1,
,
,0,
,
,1,
,
,0,
,
,0,
,
,1,
,
,1,
.
(Ⅱ)当
时,设
且
(A)
,求
中元素个数的最大值;
(Ⅲ)当
时,设
且
(A)
,求证:
中的元素个数小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8608f691fb64f578cf3ee5af3cd8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e97569e91e9574c327bab94fbd9bb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659ce142c5578c660dcadacb81b8d7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93fedde9bb8f927c986094275598b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7577c2f2038fd5478e71655277a4a853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c4974696608167ebc73d9081552d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7009fe80f51263ce2d10a09bdfea9ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6440421ef1201f1e2ad00f8bfb77964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b161ad2e118a142d9aafa2e39e30b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e1862efa4931cbf76743033ad6f1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e235caa78f940a1d9c4d0e785d425d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096409e0b9a113e1e43801cf41b3d4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d0e49177363675f01a9a754a0a62cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d533b594f63c4d48135aa0a02592b89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb900b1334149968e3a28a218ecbf7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b6a2131422a8c21784d06a21b3a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606b0d7a53aa72715af4bb9508320f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d533b594f63c4d48135aa0a02592b89a.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcca0e992d47f3db0be185ba861adf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811f2ad9bbe890879e63f151b37bb814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0204f76cda5ea4ced714588be1efeaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcca0e992d47f3db0be185ba861adf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811f2ad9bbe890879e63f151b37bb814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d415dd1391cf359512f7714d4458feee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52265b7b99204466ba6eebd6e72ba860.png)
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名校
8 . 对于一个非空集合A,如果集合D满足如下四个条件:①
;②
,
;③
,若
且
,则
;④
,若
且
,则
,则称集合D为A的一个偏序关系.
(1)设
,判断集合
是不是集合A的偏序关系,请你写出一个含有4个元素且是集合A的偏序关系的集合D;
(2)证明:
是实数集R的一个偏序关系:
(3)设E为集合A的一个偏序关系,
.若存在
,使得
,
,且
,若
,
,一定有
,则称c是a和b的交,记为
.证明:对A中的两个给定元素a,b,若
存在,则一定唯一.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ff092e72c0b8af0ec11ea1e16c20c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20ff64cc48dd0907b3f86c2f72ed4fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802a18618d983265b240d352e98010d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c87ad49613978a306ab1c000c84f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fac2c1aab61d5d6b6d1ebacf76df4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04263219b135885a77d0b95ff5ae8e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b443c138c481dfd65c9f6e003d087b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fac2c1aab61d5d6b6d1ebacf76df4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55303eac47b7521d66c984919ef73245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecf5892f45e01accf16c028f1496604.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4b90a63a63e136b98a6061d703c281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6919731148cf9c61e492ecd22944897b.png)
(3)设E为集合A的一个偏序关系,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e35231b964e293122c4383dac2431b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c0547c0182518c13ce84342425a4c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e925c95774708b58f8be28702284c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452f5111086abcdf21884aac981a260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc050f06a69d0a74c28484d3d99f8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b95219d991157bb0de786036d581b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a922973fd5aa9d110397c6ab1dce314b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d9b8041d0643aca9a58973723d3488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108d495e1cba00ecd1c2cabedd93cfd1.png)
您最近一年使用:0次
2021-03-25更新
|
1118次组卷
|
6卷引用:北京市门头沟区2021届高三数学一模试题
北京市门头沟区2021届高三数学一模试题北京卷专题02集合(解答题)(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)(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)高一上学期第一次月考解答题压轴题50题专练-举一反三系列北京市第二中学2023-2024学年高二上学期10月学段考试数学试题
名校
解题方法
9 . 对于非负整数集合
(非空),若对任意
,或者
,或者
,则称
为一个好集合.以下记
为
的元素个数.
(1)给出所有的元素均小于
的好集合.(给出结论即可)
(2)求出所有满足
的好集合.(同时说明理由)
(3)若好集合
满足
,求证:
中存在元素
,使得
中所有元素均为
的整数倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.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/911cdb689ca80557ce076cb49b3ee498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)给出所有的元素均小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)求出所有满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7a6d4b773d984df6fd1e0dce3adfb9.png)
(3)若好集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fc21f14cb5d8d28f498d35606477ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
10 . 给定的正整数
,若集合
满足
,则称
为集合
的
元“好集”.
(1)写出一个实数集
的
元“好集”;
(2)证明:不存在自然数集
的
元“好集”;
(3)是否在自然数集
的
元“好集”? 若存在,请求出所有自然数集
的
元“好集”;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dc40fc087732c80dc3d4c03abfd198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30852092007e8cac1f781f46570c8e8.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/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)写出一个实数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)证明:不存在自然数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(3)是否在自然数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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