名校
解题方法
1 . 已知
为有穷数列.若对任意的
,都有
(规定
),则称
具有性质
.设
.
(1)判断数列
是否具有性质
?若具有性质
,写出对应的集合
;
(2)若
具有性质
,证明:
;
(3)给定正整数
,对所有具有性质
的数列
,求
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78dab5f68d424caa15eb7686f8ac2249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae415a09c33aa3e9d1a3dab6c522dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7e9edf6d0468e0f8ca78b8bac63bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b740bc48c9718a294c11a1485fd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f21d7bf91134d8d08668cee5dacc2e8.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd984b8eee88a2c10df0e883c9ef67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed1adc648cc7d8fe7ac43df4b918f11.png)
(3)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-01-05更新
|
679次组卷
|
6卷引用:北京市第二中学2023-2024学年高二下学期期中(第五学段)考试数学试题
名校
2 . 已知集合
,且集合
具有以下性质:
①
中的元素有正整数,也有负整数;
②
中的元素有奇数,也有偶数;
③若
,则
;
④
.
回答下列问题.
(1)若
,求证:
;
(2)判断集合
是有限集还是无限集,并说明理由;
(3)判断0和2与集合
的关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cc4258c4462d5b975319d077ba4b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0da721a308e3e091ad85573ada57e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a288b3ba82279d7c62a49065a080d35.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c523cff49126575b264a5749fe87f3d.png)
回答下列问题.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320a7c616f6f7207a0a38bb707ac2205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e80e9b33434f0573aa5da2acf7f4d9.png)
(2)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)判断0和2与集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2022-12-03更新
|
138次组卷
|
2卷引用:北京市广渠门中学2022-2023学年高一上学期期中质量检测数学试题
3 . 已知有限数列A:
,
,…,
(
且
)各项均为整数,且满足
对任意
,3,…,N成立.记
.
(1)若
,
,求
能取到的最大值;
(2)若
,求证:
;
(3)若
(这里
是数列的项数),求证:数列A中存在
使得
.
![](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/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2477167a02872167b2a3760f09d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a6ebb915a215c07283b6d7cd8c264e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adb9024276bd7d9a5b1dbca11a9197c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cf6bff0e909bfe894d0a618b3bb9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2baac2d64b0bee4a4683f32b3078e293.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241d587c2e6f2f109a4e41b79f1c800f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba7a40102e81f5759f7b05ebf5a18c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8a0d4158a6df1bf0631095eb51c10c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb189e7f5f358b2de87dc4b93413366.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213966d4d1ceb09a181ca9318b402791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b9b60d7a248fd6b3c99bbd76000fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f24bb5c463c691eb32e7d3820c4dd5d.png)
您最近一年使用:0次
4 . 设n为正整数
,若
满足:①
;②对于
,均有
,则称
具有性质
.对于
和
,定义集合
.
(1)已知
,判断
和
是否具有性质
(直接写出结果);
(2)设
,且
具有性质
,写出一个
及相应的
;
(3)设
和
具有性质
,那么
是否可能为
?若可能,写出一组
和
;若不可能,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ce769f6795d1463744a0d74901fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556a481809009382b48169a908a8d3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e67691c95c84c3567eb5fd7d00075d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ed8bcecf6762164c9f8894942d5083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af70015e47edd3f7eeb441645283c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556a481809009382b48169a908a8d3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6b04e179e843c646481aff8f08534d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84788a8fa49ede599af521873c3a8da.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5aa46e4e3369317a2b83cbf8201b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b72283959c60b0aba983da6d65ca51a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f449a982c08087cb2e1408906468ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8147ecded7df76c941673ac8251b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7204d924d34fc81911de26a460b252.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19305744dcc72ca3997f9bc0dcdfb5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7204d924d34fc81911de26a460b252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e422fdd219db84761945e297fffb86a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
您最近一年使用:0次
5 . 对于向量
,若
三个实数互不相等,令向量
,其中
,
,
,(
).
(1)当
时,直接写出向量
;
(2)证明:对于
,向量
中的三个实数
至多有一个为0;
(3)若
,证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e5c3a589422f1b864033d402884496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636995f2a3d0002f8770cf3c4b6fb466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebbde22ed838221cd11ed36317aa123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843ff24183004a105ff0c73a1fac6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe08794bdcc386a700cf75d9bb0a255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7455cd15ac74993fb312181398b4695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd53356f1e27b6118707e9a1d13ee16.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87ee697ae9c1058d13dbf5426f7ebae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d73af1566d49cd8f69c95feae96195.png)
(2)证明:对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec36ae4ba2b370b0ec4f0444c6d3883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06234f2f106157be3d8112277feed5b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf801ce0f23ecf1a734ceb5b851253e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3d50b452aca40b6e77c2a37ff5bac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c8d56143476027f37a5eaec265ce7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c3418994990cf09d7cefbbc6f2a869.png)
您最近一年使用:0次
名校
6 . 已知集合
(
且
),
,且
.若对任意
,
,当
时,存在
,使得
,则称
是
的
元完美子集.
(1)判断下列集合是否是
的3元完美子集,并说明理由;
①
;
②
;
(2)若
是
的3元完美子集,求
的最小值;
(3)若
是
(
且
)的
元完美子集,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410a811a99d6f15164cdda4597323168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dd50a4fd2329323aa21597e8ff664b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aadf01e5fac133cf390407bfad26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d169a02afabbe304cf64b355bf71742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49972f77c4c3b89116f02cbaba7f9089.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc21b9d3aa5f307d9c9d63ffaf68dc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfbdcd7014f79de428c1d5e6525aecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0604cb71df25c9b90c5d7521d3edd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717995559c925685dacedc60be48fd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7c557b1aadac2ee7012fb1e1ba5f8.png)
您最近一年使用:0次
2022-05-12更新
|
733次组卷
|
4卷引用:北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题
北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题北京市第二中学2022—2023学年高一下学期第六学段阶段性考试数学试题重庆市杨家坪中学2022-2023学年高一上学期10月月考数学试题(已下线)专题16 数列新定义题的解法 微点2 数列新定义题综合训练
名校
解题方法
7 . 已知集合
,且M中的元素个数n大于等于5.若集合M中存在四个不同的元素a,b,c,d,使得
,则称集合M是“关联的”,并称集合
是集合M的“关联子集”;若集合M不存在“关联子集”,则称集合M是“独立的”.
(1)分别判断集合
与
是“关联的”还是“独立的”?
(2)写出(1)中“关联的”集合的所有的“关联子集”;
(3)已知集合
是“关联的”,且任取集合
,总存在M的“关联子集”A,使得
.若
,求证:
,
,
,
,
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de70a9c335265f5e4b61a2f7989e2e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd60406fc788b81ef67654138b352c7.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c44f95dd4daea270501b7c0bc0ac34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4de7b549ffad65410afe7e655df0c9.png)
(2)写出(1)中“关联的”集合的所有的“关联子集”;
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7e475e8d3a456ec527868697ea17d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d89801d24aa43f47d6a366aad0571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ccce8225324817b0577551956464f.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
您最近一年使用:0次
2022-05-02更新
|
604次组卷
|
2卷引用:北京理工附中2021-2022学年高二下学期期中考试数学试题
8 . 对于正整数
,
,存在唯一一对整数
和
,使得
,
.特别地,当
时,称
能整除
,记作
,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4920c1a7681e10fb6cadc38e97e6c550.png)
(1)存在
,使得
,试求
的值;
(2)求证.不存在这样的函数
:
,使得对任意的整数
,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
(3)若
,
(
指集合
中的元素的个数).且存在
,
,
,则称
为“和谐集”.判断:当
时,集合
中有12个元素并且含有
的任意子集是否都为“和谐集”,并说明理由.
![](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/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc44be06f0c814035e7dfe1d6b8fe64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628504e14b3c2ea172a02484a727bca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.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/a8954edf77bd075dfb0c3b97a02c55ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4920c1a7681e10fb6cadc38e97e6c550.png)
(1)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a55fa242ba35478b111f2bbffac589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767992f5013f9e1b4d37e51f884d3640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求证.不存在这样的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c7403a619d584956f21284ddc23fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3830ea6ea58c99a0fc1adadccac0fab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b364ee7c2d8705c4efd99da8184ef4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf34614d82a90cc1e587eaa5e11753e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9195b943cc9f227f6affa59a601cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b5393742efe51da907dd21e66618bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5556dd86322752a457b3a6ba979c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8954edf77bd075dfb0c3b97a02c55ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caddd958ae597c7a1f8f6a9ee2a3200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-04-09更新
|
211次组卷
|
2卷引用:北京市第五中学2021-2022学年高一下学期期中考试数学试题
名校
9 . 定义:给定整数
,如果非空集合满足如下3个条件:①
;②
;③
若
, 则
;则称集合
为“减
集”.
(1)
是否为“减
集”?是否为“减
集”?简要说明理由;
(2)证明:不存在 “减
集”?
(3)是否存在“减
集”?如果存在,求出所有“减
集”;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc7338b2a8a4a7d06acd6eb1b446564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b79c9010218563cb4fd0bc9b1202ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520eacf429c406544c48df40a46c1035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45251c3475305d50c946539a1bd6a5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e5f130f1e3537857a5e4265498e491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)证明:不存在 “减
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(3)是否存在“减
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
10 . (1)已知
,证明:
;
(2)用反证法证明:三个数中
至少有一个大于或等于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406040aef525784bbe68b2501947fa7c.png)
(2)用反证法证明:三个数中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e6a8e3f3ac3af2452dad7ad1e37a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf3f23bfec394769b4670962b219999.png)
您最近一年使用:0次