名校
1 . 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)
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2021-03-25更新
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6卷引用: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
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
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2 . 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
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21卷引用: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)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)(已下线)1.3 交集、并集(已下线)专题01 集合与逻辑(讲义)-2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)(已下线)集合及其运算
3 . 对于由m个正整数构成的有限集
,记
,特别规定
,若集合M满足:对任意的正整数
,都存在集合M的两个子集A、B,使得
成立,则称集合M为“满集”,
(1)分别判断集合
与
是否为“满集”,请说明理由;
(2)若
由小到大能排列成公差为d(
)的等差数列,求证:集合M为“满集”的必要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5fdf0e4f9de36f08402dd96d237e.png)
或2;
(3)若
由小到大能排列成首项为1,公比为2的等比数列,求证:集合M是“满集”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e495e34870eb6eef8486f88e567c7e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9cd59e58555bfc92257ba31d16794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44aed8cc107aecae26873891bfdc5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf084cdb896062c63e919adf38352d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01a90899f08d43e7f1b945b96aae753.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4804e8c356d6aa5b0d645fed77fec88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5d150c4bf3836b14db9cd1017aeacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e789387bf82c893b83cb8f2007f060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f5fdf0e4f9de36f08402dd96d237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f0913464ddee73888f859ec6ad1696.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
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2020-12-27更新
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4卷引用:北京市人大附中朝阳学校2020-2021学年高二下学期数学统测试题
北京市人大附中朝阳学校2020-2021学年高二下学期数学统测试题上海市松江区2021届高三上学期期末(一模)数学试题上海市松江区2021届高三高考数学一模试题(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮
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4 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1edda0a840fa9fd056a84b3851fe2840.png)
,其中
,定义
.若
,则称
与
正交
(1)若
,写出
中与
正交的所有元素
(2)令
.若
,证明:
为偶数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1edda0a840fa9fd056a84b3851fe2840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc70211f57c2993d7047c89fd3fc2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb56545f5200342abd9e406cb200328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9117bd5df08f7f5cf00d1bd3ced32e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157967918cabbed7f5d82a291cc262f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b623d5f3c82cfdc60c0d74f381e6e1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4bd27eda92741b7923451594321771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22111b1f07e7873e5a156d1937eaac27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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5 . 已知
是满足下列条件的集合:①
②若
,则
,③若
且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
是否正确,说明理由
(2)证明:若
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c4dffdf9c06c0d11d0410f194afc8c.png)
(3)证明:若
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f17b77451caf220bd4808446c5c79e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c443466385f21cd3f06e2e4229add79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3143beb0df5feff68bf6dd94fdfd6b5b.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c4dffdf9c06c0d11d0410f194afc8c.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f06a4a9deb51418c20e7e7376cc807.png)
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2020-10-23更新
|
584次组卷
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6卷引用:北京师范大学附属中学2019-2020学年高一上学期数学第一次月考试题
北京师范大学附属中学2019-2020学年高一上学期数学第一次月考试题北京市海淀区北京医学院附属中学2021-2022学年高一10月月考数学试题上海奉贤区曙光中学2020-2021学年高一上学期10月月考数学试题沪教版(2020) 必修第一册 精准辅导 第1章 1.1(1) 集合(已下线)1.1集合初步(第1课时)-高一数学同步精品课堂(沪教版2020必修第一册)(已下线)1.1 集合的概念及特征(精练)《一隅三反》系列
名校
6 . 数字
的任意一个排列记作
,设
为所有这样的排列构成的集合.集合
任意整数
都有
,集合
任意整数
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9d89f2b4a2e160458b36c8fd270c89.png)
(1)用列举法表示集合
;
(2)求集合
的元素个数;
(3)记集合
的元素个数为
,证明:数列
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1862403f59a94ecf2d21fe7e19d2aec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c686124767ab3c2b84470b065fcef89b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7bc57de21efd7fa1776a01591d99a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12df2ae8d3e915feafa1c5c21f2926e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767965df8401842b4d727998d43a4fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280a824d01ca8de7247b6e2ddd6fffdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e2febfa043de68251b23704c5e420a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9d89f2b4a2e160458b36c8fd270c89.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f266dacf74b0a86d671a5a422f848cb9.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c612f58462180705a1acfd433714a4.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2020-04-03更新
|
712次组卷
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4卷引用:2020届北京市清华大学附属中学朝阳学校高三第一学期第二次质量检测数学试题
7 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3da1622fd45abbb7c8de0c88e7956e.png)
,对于
,
,定义A与B的差为
;A与B之间的距离为
.
(I)若
,试写出所有可能的A,B;
(II)
,证明:
(i)
;
(ii)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2814197b2f57be423f756e7f5cd8c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d00142a30916b2c563b15d4ef4cd5c.png)
三个数中至少有一个是偶数;
(III)设
,
中有m(
,且为奇数)个元素,记P中所有两元素间距离的平均值为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3da1622fd45abbb7c8de0c88e7956e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ce769f6795d1463744a0d74901fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932e8ec84cfecd3642e74fa987d789af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c76f1774902da4c8da18791b5a35c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f960a435af66d6f53c96cf5d0d7ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2323a679e8e151769dd5dda4678de22.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91753ab4b8edae53e1947f25d3a0bddd.png)
(II)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5318f129bfbfca89f51c03144251ce79.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8513f18376e4e456b939d0f1cdb6e602.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2814197b2f57be423f756e7f5cd8c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d00142a30916b2c563b15d4ef4cd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab2029064842c2c77fc20f69c402cd6.png)
(III)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2b280a6a65c9bf2f20cad5d1106080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bda892497cea43df67db57b4e2a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a3abd64b3a560384a51e2d7c171aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc589d2e2848264dd6c1fdb18ae91b2.png)
您最近一年使用:0次
2020-04-28更新
|
725次组卷
|
2卷引用:2020届北京市朝阳区六校联考高三年级四月份测试数学试题A
名校
8 . 对于集合
,定义函数
对于两个集合
,
,定义运算
.
(1)若
,
,写出
与
的值,并求出
;
(2)证明:
;
(3)证明:
运算具有交换律和结合律,即
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6897439ed76144996f77405e800fd67b.png)
对于两个集合
![](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/42e7e34beaff39ac5d8f3c7898804380.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc97700060520fb568f5aca7256b193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cea70b4969a5494ceb845f1818c26b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c55c7b14727415d05ed3557918ac38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5231cb0bfedf2f963c1830adfd74aa.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859bd72898c667a3e4c6976b6dcb020e.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7d51315fcca519cb58bacd0040d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b4388c3b893c55b81e2b15ec4fa9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccff813e57fa8b0fb3649da671dc52b.png)
您最近一年使用:0次
2020-01-19更新
|
356次组卷
|
3卷引用:北京市日坛中学2023-2024学年高一上学期12月月考数学试题
9 . 设集合
的元素均为实数,若对任意
,存在
,
,使得
且
,则称元素个数最少的
和
为
的“孪生集”;称
的“孪生集”的“孪生集”为
的“2级孪生集”;称
的“2级孪生集”的“孪生集”为
的“3级孪生集”,依此类推……
(1)设
,直接写出集合
的“孪生集”;
(2)设元素个数为
的集合
的“孪生集”分别为
和
,若使集合
中元素个数最少且所有元素之和为2,证明:
中所有元素之和为
;
(3)若
,请直接写出
的“
级孪生集”的个数,及
所有“
级孪生集”的并集
的元素个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2317480af8719266bb92ee59d6b2c3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f502064e70176f25ed0e1c29c979a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd9271372676f33ffe81bbd9dde52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb573197384b9410cb951a4d1e301b3c.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/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72bc3ebd480e761d156ae995abc1153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设元素个数为
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3efe261376149359971ac137d88f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00ab72facda02139df8dadc8dbea3a6.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
您最近一年使用:0次
名校
解题方法
10 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-02-01更新
|
577次组卷
|
6卷引用:北京市密云区第二中学2024届高三上学期10月月考数学试题
北京市密云区第二中学2024届高三上学期10月月考数学试题上海市七宝中学2020届高三上学期11月月考数学试题北京市东城区景山学校2021届高三上学期期中数学试题上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题上海市曹杨二中2019-2020学年高二上学期期末数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21