名校
1 . 记集合
.对任意
,
,记
,对于非空集合
,定义集合
.
(1)当
时,写出集合
;对于
,写出
;
(2)当
时,如果
,求
的最小值;
(3)求证:
.
(注:本题中,
表示有限集合A中的元素的个数.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a89f895a14b4f202dfe6b19224857c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c86c0b2a71ee538df6ab1eab3c8b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd58ba2338450bd94bc2a1ec0a0a51ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120df58b92e747fc3091f1a3aeff228d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13342dd73eb34ca37aaca5b521706442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ca324ae5ead82dd03b6cb5afac67a5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4469a0542c773e329e8cc42e14a84169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ca0b9e99203ec575c46cdbf2d4ef0d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8839c83b988c42da1fce4a96787583eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25376e139f40d0df5ada2c9ebb1da2e4.png)
(注:本题中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
您最近一年使用:0次
名校
2 . 已知集合
,其中
且
,非空集合
,记
为集合B中所有元素之和,并规定当
中只有一个元素
时,
.
(1)若
,写出所有可能的集合B;
(2)若
,且
是12的倍数,求集合B的个数;
(3)若
,证明:存在非空集合
,使得
是
的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbde10b7bc82536072ca38f32b2f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe11d564517c04437b9884da859002b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bc3a22bc9cb056df1e6d5218877c8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6e90ea92c80c31653e4ac972bf56c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d725be6acff620b47bb7a8a7a0c6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5e68b8592c14157df8db05904c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
2024-01-20更新
|
320次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
3 . 已知点集
.设非空点集
,若对
中任意一点
,在
中存在一点
(
与
不重合),使得线段
上除了点
外没有
中的点,则
中的元素个数最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b22251511d66ad0c49513dae61f2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fcd91711251a8bfe28b22c870dad80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fb56e714978b3dd418996c1f75768c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
名校
解题方法
4 . 已知
为实数数组,定义集合
,给定正整数m,若
,则称A为
连续生成数组.
(1)判断
是否为
连续生成数组?是否为
连续生成数组?说明理由;
(2)若
为
连续生成数组,求
的值,并说明理由;
(3)数组
是否为
连续生成数组?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ae7c0278483549695d65b1faf5d856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a9856e71c2235898b9ae8dd5b511df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66383c85540d787a9554f881e2599383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb654dbe976f077495105b21b7963d0f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4527a28b17b82e1a9c4036294529ba6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3071dd7848459f70f912d758466b12b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da92a00c5e0121accc325e50f6492fe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b94c86d13f5934d26b946c119e28f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da92a00c5e0121accc325e50f6492fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ae7c0278483549695d65b1faf5d856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105a4a76bb426a85ba65255ded2147f3.png)
您最近一年使用:0次
名校
5 . 设有限集合
,对于集合
,给出两个性质:
①对于集合A中任意一个元素
,当
时,在集合A中存在元素
,使得
,则称A为
的封闭子集;
②对于集合A中任意两个元素
,都有
,则称A为
的开放子集.
(1)若
,集合
,判断集合
为
的封闭子集还是开放子集;(直接写出结论)
(2)若
,且集合A为
的封闭子集,求
的最小值;
(3)若
,且
为奇数,集合A为
的开放子集,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d3d592c03146bab0e93fee04ad3072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e827f67d8b6f601f25c39c0116abda42.png)
①对于集合A中任意一个元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6f4f0f0f629dae342af9261c006de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17748c68c2a8a738c52175ebaa2f5e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247d742bdd34642e1da9fe9161e3a637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
②对于集合A中任意两个元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a843998f766e61f7abbdd2e985bad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb52fdd006724b2dfdb7e6988f813ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb2ad93be53f0838c8563903ad31b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20a5ff55592f7eea41b0ef0d8cd7f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a994566930068fd6edf5342c69bc25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e586121ce8e638b9d8da6d3a00f308ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-01-06更新
|
747次组卷
|
9卷引用:北京市昌平区2022-2023学年高一上学期期末质量检测数学试题
北京市昌平区2022-2023学年高一上学期期末质量检测数学试题北京市第一六六中学2022-2023学年高一下学期阶段性诊断考试数学试题北京市第一六六中学2022-2023学年高一下学期3月月考数学试题(已下线)1.1集合的概念(分层作业)-【上好课】(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)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02集合间的基本关系2-【倍速学习法】(人教A版2019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
解题方法
6 . 集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbcace4afbfc0f54dcc48bb0027421d.png)
,其中
为正整数.对
中的任意元素
和
,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4792cb732db55a4e316194b8dce162.png)
(1)当
时,求
和
的值.
(2)当
时,
的子集
满足:对
中任意元素
和
不能被
整除,且当
时,
能被
整除.求集合
中元素个数的最大值.
(3)给定
的子集
满足:对
中任意元素
和
,当
不等于
时,
.求集合
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbcace4afbfc0f54dcc48bb0027421d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6560671eeefa4dbeffee99e5b6cbb340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862fa87bae8adc1812c8a388540ffeab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e44f3369474465aead73a72de28e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4792cb732db55a4e316194b8dce162.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf566d23dea97f8fe28cebd1ed1f6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b55e4da087f72dbae9e2b267fe8d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f96befc97fd01907c8ee93b77654e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5946132021868ed3dd54f1c8ff8f13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f96befc97fd01907c8ee93b77654e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)给定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c56eb0dd21760e45b92fbe0e3098786.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.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/bdff4c5bc8d38fdf36c1887e4c72f373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
7 . 对任何非空有限数集
,我们定义其“绝对交错和”如下:设
,
,其中
,则
的“绝对交错和”为
;当
时,
的“绝对交错和”为
.若数集
,则
的所有非空子集的“绝对交错和”的总和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95526bf7a8da1b4fbfa1d67805fac12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f5f2024c63910786f10e6520a775fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bd9ff0d9a03b989603938e63f3a961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d6492ee1c0f35c492cf71938907fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8d40e257f9c446b8e30fa841b74bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f49fa2986b7bff2bceae51804a9260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 定义:若任意
(m,n可以相等),都有
,则集合
称为集合A的生成集;
(1)求集合
的生成集B;
(2)若集合
,A的生成集为B,B的子集个数为4个,求实数a的值;
(3)若集合
,A的生成集为B,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f9849615359e0d43a363c88c537e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7dbb35ab5ab3303507508787d07714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea53a7f620b436b9983ab6c836213c6.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d94174816d8ac2c555deda4d2d913f2.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6bd4f4d19deb06c14ffcf1e6e93910.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd428c972128a61b81f45ba9d9fbff5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
您最近一年使用:0次
2021-11-15更新
|
1191次组卷
|
13卷引用:北京市第五十中学2022-2023学年高一上学期10月月考数学试题
北京市第五十中学2022-2023学年高一上学期10月月考数学试题北京市朝阳区中国科学院附属实验学校2023-2024学年高一上学期9月月考数学试题上海市奉贤中学2021-2022学年高一上学期期中数学试题(已下线)突破1.2集合间的基本关系(课时训练)(已下线)上海市华东师范大学第二附属中学2022-2023学年高一上学期开学考试数学试题上海市进才中学2022-2023学年高一上学期10月月考数学试题上海市甘泉外国语中学2022-2023学年高一上学期阶段性检测数学试题(已下线)期中模拟预测卷01(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)(已下线)第02讲 集合间的基本关系(4大考点7种解题方法)(3)上海市南汇中学2022-2023学年高一上学期10月月考数学试题(已下线)1.2集合间的基本关系(分层作业)-【上好课】(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(沪教版2020必修第一册)湖南省邵东市创新学校2023-2024学年高一上学期2024级特训班第一次月考数学试题
名校
9 . 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)
您最近一年使用:0次
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