解题方法
1 . 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)
您最近一年使用:0次
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解题方法
2 . 定义:给定整数i,如果非空集合满足如下3个条件:
①
;②
;③
,若
,则
.
则称集合A为“减i集”
(1)
是否为“减0集”?是否为“减1集”?
(2)证明:不存在“减2集”;
(3)是否存在“减1集”?如果存在,求出所有“减1集”;如果不存在,说明理由.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc7338b2a8a4a7d06acd6eb1b446564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebabd7323bae39388835a33e09046c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669926e4732ba3eca48e018aaebe7079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45251c3475305d50c946539a1bd6a5f8.png)
则称集合A为“减i集”
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed72c5ada5b4d689310406b7cef32f.png)
(2)证明:不存在“减2集”;
(3)是否存在“减1集”?如果存在,求出所有“减1集”;如果不存在,说明理由.
您最近一年使用:0次
2020-03-14更新
|
1147次组卷
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7卷引用:2020届北京市中国人民大学附属中学高三开学复习质量检测数学试题
2020届北京市中国人民大学附属中学高三开学复习质量检测数学试题(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)北京市海淀区中国人民大学附属中学2023届高三下学期开学摸底练习数学试题北京市人大附中2023届高三下学期2月开学考数学试题(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)北京市海淀区宏志中学2023-2024学年高一上学期期中考试数学试卷重庆市西南大学附属中学校2023-2024学年2023-2024学年高二下学期3月测试数学试题
3 . 给定整数
,记
为集合
的满足如下两个条件的子集
的元素个数的最小值:ⅰ.
,
;ⅱ.子集
中的元素(除1外)均为
中的另两个(可以相同)元素的和.
(1)求
的值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6a1d0b6255d2fe84bfad2e4ad232d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006862363f0414fa9eaa25411bfbc1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd61ca77c54e98408bd4bfe5898671b.png)
您最近一年使用:0次
2018-12-14更新
|
215次组卷
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3卷引用:2012年新知杯上海市高中数学竞赛试题