名校
1 . 设集合
,满足下列性质的集合称为“翔集合”:集合至少含有两个元素,且集合内任意两个元素之差的绝对值大于2.则A的子集中有___________ 个“翔集合”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c888363bcc23fb20f3a36ba34f0a7d7d.png)
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2021-09-16更新
|
1468次组卷
|
5卷引用:全国高中数学联赛模拟试题(十四)
全国高中数学联赛模拟试题(十四)浙江金华第一中学2022-2023学年高三下学期3月月考数学试题湖南省岳阳市2022-2023学年高一下学期期中数学试题(已下线)人教A版高一上学期【第一次月考卷】-【满分全攻略】(人教A版2019必修第一册)(已下线)新题型02 新高考新结构竞赛题型十五大考点汇总-1
名校
2 . 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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名校
3 . 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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c9e547b17582b99e548037172eeff3.png)
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n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/95c9e547b17582b99e548037172eeff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677fd74842cbce34aed7073cebbd9c58.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n为偶数且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.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)
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2024-03-12更新
|
448次组卷
|
2卷引用:北京市第八中学2023-2024学年高三下学期3月月考数学试题
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)
您最近一年使用:0次
名校
5 . 对于任何给定集合S,用
表示集合S的元素个数,用
表示集合S的子集个数.已知集合A,B,C满足下列两个条件:①
,②
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f49911a4a2a1eb5a4cc72185d111c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65093c32706d98ddd3def30c4a95cc3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c64ab7605924a5a30f60c01658e253d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac0a63e011dbe44cc967f8585b0eceb.png)
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名校
6 . 设整数集合
,其中
,且对于任意
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d226dbccd278f6d20653d52c4fe28351.png)
(1)请写出一个满足条件的集合
;
(2)证明:任意
;
(3)若
,求满足条件的集合
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a02459a21167382ebfb095935255cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f947cf70804570839084fb9e8ffdad3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b836bde5106e78caeb728ff3353bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269c7a915fc171ac7ad84c09883a6dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d226dbccd278f6d20653d52c4fe28351.png)
(1)请写出一个满足条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)证明:任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484fc0329e7b476cd093d844d09fb20f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5215a6d2915d87bbc65302d184df8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2020-01-13更新
|
934次组卷
|
3卷引用:北京市西城区2019-2020学年高三上学期期末数学试题
7 . 设
且
,集合
的所有
个元素的子集记为
.
(1)求集合
中所有元素之和
;
(2)记
为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
中最小元素与最大元素之和,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32124e425314792de0a78c4aab9dc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44417455b9cc30693d09cbcfe4ed97c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a584b6ad5577ab3e2d22caf23e3c32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835e8c3900cb61bc8ddc313d5ce2253d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f0f2e18a330acee267e6f44319ef96.png)
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解题方法
8 . 已知集合
,
,
,若
,
,
或
,则称集合A具有“包容”性.
(1)判断集合
和集合
是否具有“包容”性;
(2)若集合
具有“包容”性,求
的值;
(3)若集合C具有“包容”性,且集合C的子集有64个,
,试确定集合C.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe38d1b1e18720a878bd7442c8f094de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46de01c5104b9112a688df37eadb000.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac46c6c52fc8b8e8f76084352e1893f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3ed03b0f8fb8b88d7edf6165345c6f.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acf45d9d64697db902fe8faa15394d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
(3)若集合C具有“包容”性,且集合C的子集有64个,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65f44d4f1341a7d80897a54a6778fae.png)
您最近一年使用:0次
名校
9 . 若集合
,集合
,其中
,则称集合
是集合
的一个“
元子集”.若“
元子集”
中的元素
满足对任意
,恒有
,则称
为
的一个“个性独立子集”.已知集合
,集合
是
的一个“个性独立子集”.
(1)求所有满足条件的集合
的个数;
(2)若
且互不相等,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b7c647eb8e6be44689333e1a6f1f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ed4e9293f5066fe367cfa541afa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d87fa699e2aca137f69e4ac0883dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4aecf0b7edfa826f73389322a52cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c01531dd639f0ad3da0098febbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effaffc8a4d01f865a79933d3c337060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求所有满足条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3fa353ea21d2dea55e32a354e3dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0736f73b81bec1c5d4efe968cfbe2a.png)
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10 . 若集合
的非空子集
满足:对任意给定的
,若
,有
,则称子集
是
的“好子集”.记
为
的好子集的个数.例如:
的7个非空子集中只有
不是好子集,即
.记
表示集合
的元素个数.
(1)求
的值;
(2)若
是
的好子集,且
.证明:
中元素可以排成一个等差数列;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5c44de003475d3466981293cf5e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c469f6345826410959ea09d7e3192e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0586ec8d1d9796fb80a1250e2c0a4b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c562f247c1d691158f4038a030574c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68eafd45c1ec4b414d3553dabd8c2848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37765d2927d24d4b582423c843aebcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada01c2a8b4d92df94834a6a3929673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df6a6d73a058d13632a726c2308d66.png)
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