名校
1 . 已知集合
,若集合
满足
且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfaf2133a57a1ba37929353a7e872b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e544b1304a6bbc87283cf741f134cebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503063d36255ecb333cec1f27ec69b63.png)
A.![]() | B.![]() |
C.集合![]() | D.集合![]() |
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解题方法
2 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若
为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377240e8ad277805e0499803d5be5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623eef12f37f0b85ddd367faa9b3bfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
您最近一年使用:0次
2023-05-28更新
|
718次组卷
|
12卷引用:北京市第二十中学2022-2023学年高二上学期12月月考数学试题
北京市第二十中学2022-2023学年高二上学期12月月考数学试题北京市西城区2021届高三5月二模数学试题北京市第五十七中学2021-2022学年高二上学期期中检测数学试题北京一零一中学2023届高三下学期数学统练四试题北京卷专题02集合(解答题)北京市第一0一中学2022-2023学年高三下学期统练数学试卷(四)(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北京师范大学第二附属中学2023-2024学年高二上学期期中测试数学试题北京市东城区景山学校2024届高三上学期12月月考数学试题北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)拔高点突破01 集合背景下的新定义压轴解答题(四大题型)
名校
3 . 已知集合
,
,若
且
,则M的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0945b9f47f37e913573a970c9c0f66e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30111cd9c9d633690af67ae7b5a375c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9b19e8ecf30ff55c093c894f78b742.png)
A.1 | B.3 | C.4 | D.6 |
您最近一年使用:0次
2022-11-17更新
|
255次组卷
|
2卷引用:江苏省苏州市六校2022-2023学年高一上学期期中联考数学试题
名校
4 . 对于集合
,定义
,设
.
(1)设
,
,求
,
;
(2)若
是S的子集且
,求满足条件的
的个数;
(3)设
是正整数,若对S的任意一个
元子集
,都有
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae176533a8607eb2ebc48bc767529e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516ca1c6590a671862a47f5bb2fd8fb4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0705f5c8d67b4947455fc01be02b8a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cbc3a23934d36bd7f24ea81e8dadc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216c01a450f47b6ea550d8f54d4861d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a829cbbae2030c4e05d22cfadc31073.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0c0989448ea6be3ddc96587ea03124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab293d534f3615cc02a192fa3bd7f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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5 . 若集合
有且仅有两个子集,则实数k的值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeef789a1469eb927faf27138da2373e.png)
您最近一年使用:0次
2022-10-22更新
|
565次组卷
|
6卷引用:河南省郑州市郑州外国语学校2022-2023学年高一上学期10月月考数学试题
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6 . 从集合
的子集中选出4个不同的子集,需同时满足以下两个条件:①
、U都要选出;②对选出的任意两个子集A和B,必有
或
.则选法有___________ 种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5afb74291a8e01b3dcae940798df3fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0f24d1daf9447a4837e7886261c592.png)
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解题方法
7 . 设自然数
,若由n个不同的正整数
,
,…,
构成的集合
满足:对集合S的任何两个不同的非空子集A、B,A中所有元素之和与B中所有元素之和均不相等,则称集合S具有性质P.
(1)试分别判断在集合
与
是否具有性质P,不必说明理由;
(2)已知集合
具有性质P.
①记
,求证:对于任意正整数
,都有
;
②令
,
,求证:
;
(3)在(2)的条件下,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192fc415cb8db504ffb1ad939981b7a2.png)
(1)试分别判断在集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869ae0235255b84ece86c8bd81939067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc5cbe002e669214c4c1597bc8b0caf.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192fc415cb8db504ffb1ad939981b7a2.png)
①记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31295a254d093889374c947aa881a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87270dc51105d272c6f76af461d08457.png)
②令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9ca7e90d47d7ee295338bbac2d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa81f4cef9531213df1b3261295508eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1557d3b215f58330d34827b134ad2925.png)
(3)在(2)的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749877d42d1984fb42369b7bb4e376c7.png)
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8 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f785ab2e824114a3c9b90498bc3034.png)
,则满足
且
的集合N的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f785ab2e824114a3c9b90498bc3034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/501adaa9c7a385b2e0f3e7ec0f4110a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad96b50521f4bbf3d436d05dc258083d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d5b1b24e2d918646afd0e16e119698.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
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解题方法
9 . 已知集合
.
(1)当
时,求
的非空真子集的个数;
(2)若
,求实数
的取值范围;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc3ca24d426d64d791e96315760f5cb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834d908ef48ee95eb35811f16936541b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbbe46a98a8fdebfc46fcbc45dc88e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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10 . 设集合
,集合
,如果对于任意元素
,都有
或
,则称集合
为
的自邻集.记
为集合
的所有自邻集中最大元素为
的集合的个数.
(1)直接判断集合
和
是否为
的自邻集;
(2)比较
和
的大小,并说明理由;
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbad957385c90ca3a76e717e4b4e7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cd2449f6ae27a72287be95a661d8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320a7c616f6f7207a0a38bb707ac2205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbcd3d6b77c949be81a946ac9ed9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73707750f88b56101446fce394e0faf.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/4f7f71b0119f257edb8d5060a810de92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)直接判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4047b80385ef60ea5e9a1f184e7b948b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecde0085a473948c061942a1728a37c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64927a98d33b49dc5c6a0e65e5e8eb53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41788e238eff245e567b58dea3a0003.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f4f09e879e859a946b2d5e2d844342.png)
您最近一年使用:0次
2021-07-15更新
|
898次组卷
|
7卷引用: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)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)北京市八一学校2020-2021学年高一下学期期末数学试题(已下线)1.2 集合间的基本关系-2021-2022学年高一数学尖子生同步培优题典(人教A版2019必修第一册)(已下线)期末重难点突破专题01-【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)高一上学期期中考试解答题压轴题50题专练-举一反三系列重庆市万州第二高级中学2023-2024学年高一上学期10月月考数学试题 (已下线)专题01 集合与常用逻辑用语3-寒假作业单元合订本