12-13高一上·北京·期末
名校
1 . 已知集合
,若集合
,且对任意的
,存在
,
,使得
(其中
),则称集合
为集合
的一个
元基底.
(1)分别判断下列集合
是否为集合
的一个二元基底,并说明理由;
①
,
;
②
,
.
(2)若集合
是集合
的一个
元基底,证明:
;
(3)若集合
为集合
的一个
元基底,求出
的最小可能值,并写出当
取最小值时
的一个基底
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806fb311a1ddd23364eb67dc6eaf9aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb33db56afdfe2e6b023d001b8c7314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a347b942334e794abc5d1a583e8b434d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64950c9fd9dc31394b2e00401d1b70ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ad20a92aea25d3d1800ec6cb93699c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)分别判断下列集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453c0f95e052beb1edece487d9cab07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522954ce536d559cf03638d87fad504c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4863b95f36a4af59514b7c77e02e30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3757ba09c1d5ceb4632a8ddd47230902.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2413015bd5826b340903708cc7750a0b.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc98f4e6c9f9a1dc1080d0e0998fc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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15卷引用:上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市进才中学2020-2021学年高二下学期期末数学试题(已下线)北京市第四中学2023届高三阶段性考试(零模)数学试题北京市汇文中学教育集团2022-2023学年高二下学期期中考试数学试题北京市广渠门中学2022-2023学年高二下学期期中考试数学试题北京市第五十七中学2022-2023学年高二下学期期中测试数学试题北京市第二中学2022-2023学年高二下学期第六学段(期末)考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)2011-2012学年北京市育园中学高一第一学期期末考试数学北京市第二中学2020-2021学年高一下学期期末数学试题北京市清华大学附属中学2022届高三下学期数学统练6试题北京市丰台区丰台第二中学2023届高三上学期12月月考数学试题(已下线)计数原理与排列组合【北京专用】专题05计数原理(第二部分)-高二上学期名校期末好题汇编(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
2 . 已知集合
,对于集合
的非空子集
.若
中存在三个互不相同的元素
,
,
,使得
,
,
均属于
,则称集合
是集合
的“期待子集”.
(1)试判断集合
,
是否为集合
的“期待子集”;(直接写出答案,不必说明理由)
(2)如果一个集合中含有三个元素
,
,
,同时满足①
,②
,③
为偶数.那么称该集合具有性质
.对于集合
的非空子集
,证明:集合
是集合
的“期待子集”的充要条件是集合
具有性质
;
(3)若
的任意含有
个元素的子集都是集合
的“期待子集”,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a32bb35170ebe4aba4d96ad30fcfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1176ec378d071e8972ffaa3f944952.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/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)试判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca1c611cfb42aba676bc20f876f8f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570507469628d759e4ebf323fadf79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)如果一个集合中含有三个元素
![](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/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d561cdf17d3a6d7d57af719cb6100c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55de080a3c1313bbd6ea5c17307c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18392c5a07408fd70ddee8a30f705305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6卷引用:第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)
(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)北京市丰台区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题01集合与常用逻辑(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21北京卷专题02集合(解答题)
名校
3 . 已知集合
,规定:若集合
,则称
为集合
的一个分拆,当且仅当:
,
,…,
时,
与
为同一分拆,所有不同的分拆种数记为
.例如:当
,
时,集合
的所有分拆为:
,
,
,即
.
(1)求
;
(2)试用
、
表示
;
(3)设
,规定
,证明:当
时,
与
同为奇数或者同为偶数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb813e225b094c636d38d0e0cfbd67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea40e6c6055a63e7934f614e878940ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c3c3b06e4d829c5967bd76ab3d14ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ff4c4d26a22d8ab9e6a70cadf6623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28faa23f36fcfc2aef9cc68f46b1c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f15fa1bab95c647f87cedab26b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdc216147253ff9697788764dc1ab93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a871a43ca9e77e26f5c6b680c165e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b704d8979f50009bcb3ec36a07864d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1fdd193767192adc5adcd772ae2b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da1c8d2d0ddab6eed4da334b0446849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a045201f479d99c868e5bac5632b211.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe036f3bc2712beea23557116fdac74c.png)
(2)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8a97f873310fac16b20d730f7c4e29.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9acc25eced79e4d6973d2edeb5628c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ba78808895f5e4bd393fe7aa5b9a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bb215f28e5eea7ff4c7ca5ee9e2216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-02-07更新
|
1135次组卷
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8卷引用:6.5二项式定理(分层练习)-2022-2023学年高二数学同步精品课堂(沪教版2020选择性必修第二册)
(已下线)6.5二项式定理(分层练习)-2022-2023学年高二数学同步精品课堂(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(基础、常考、易错、压轴)分类专项训练-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市实验学校2022-2023学年高二上学期期末数学试题(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)(已下线)期中考试押题卷(考试范围:第6-7章)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)单元测试B卷——第六章 计数原理
名校
解题方法
4 . 设A是非空实数集,且
.若对于任意的
,都有
,则称集合A具有性质
;若对于任意的
,都有
,则称集合A具有性质
.
(1)写出一个恰含有两个元素且具有性质
的集合A;
(2)若非空实数集A具有性质
,求证:集合A具有性质
;
(3)设全集
,是否存在具有性质
的非空实数集A,使得集合
具有性质
?若存在,写出这样的一个集合A;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72552b86b4558a36aac78c7148d6a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4970b63e04ae03e833bdb95bd52e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出一个恰含有两个元素且具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)若非空实数集A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(3)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8afa6857b5eaf945d14a6e4d7e5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
您最近一年使用:0次
2022-11-17更新
|
647次组卷
|
7卷引用:专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)
(已下线)专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)专题01集合与逻辑(15个考点)(1)北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题(已下线)专题1.8 集合与常用逻辑用语全章综合测试卷(提高篇)-举一反三系列(已下线)重难点01集合与常用逻辑用语(9种解题模型与方法)(1)北京市东城区2021-2022学年高二下学期期末统一检测数学试题
解题方法
5 . 设全集
,集合A是U的真子集.设正整数
,若集合A满足如下三个性质,则称A为U的
子集:
①
;
②
,若
,则
;
③
,若
,则
.
(1)当
时,判断
是否为U的
子集,说明理由;
(2)当
时,若A为U的
子集,求证:
;
(3)当
时,若A为U的
子集,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fefd9d7303a04708b4f2d728e78361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed0c7122ffdbf145d72a310671465fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0412e8d25fa4748e3f6784611bd61990.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8a1b0b32229f6a9f5b85c11f05bee2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658f2824532e5b72962fe34a22c27c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251a5b0faec4a29eff8173a633c0b765.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8489b7692d3889aede2335c3ac8aca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb76e516509e33dc0d29663cc6b884bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd131b82e404452880d7a97792f22493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7844925f9077aa32c990fc20a51467.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcd23a8020d731bd512bb8df45ea594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e13bbde03ffad05ecc3fee8120b6a6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575c2057865186fb80a50f67ee6ea70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
您最近一年使用:0次
2023-01-06更新
|
899次组卷
|
10卷引用:第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)
(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)北京市朝阳区2022-2023学年高一上学期数学期末试题北京市第五十七中学2022-2023学年高一(1+3科技创新试验班)下学期期中考试数学试题(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)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(已下线)专题03集合的运算-【倍速学习法】(人教A版2019必修第一册)(已下线)第一章 集合与常用逻辑用语(单元提升卷)-【满分全攻略】(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(已下线)FHsx1225yl138
名校
解题方法
6 . 对于实数构成的集合
.若对任意
都有
(其中“
”表示普通的乘法运算),则称集合
对“
”是封闭的.
(1)已知集合
,判断
是否属于集合
;
(2)在(1)的条件下,若
,证明
的充要条件是
;
(3)若集合
对“
”都是封闭的,试判断
是否对“
”封闭,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af42f2ec410ad1b28be69d3415ed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9f1ff137e76626b7b608cef7c36349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dae68b646f975a8a0c6bed67d028ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57ed82958abb00776e75987aa62d723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ecef225b27b5857d2d76fbe5b34982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff58fdfe14af9fb8aa0e0cf0d60853a.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3375139541ed61929fa658f16bb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
您最近一年使用:0次
名校
7 . 求已知集合
,且
,
,其中
,且
.若
,且对集合
中的任意两个元素
都有
则称集合
有性质
.
(1)判断集合
是否具有性质
;
(2)若集合
具有性质
.
①求证:
的最大值大于等于
;
②求
的元素个数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99644ae5f50e3871306cf0a192829e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722bdd9ed9e5c8a2aeed8849522c0847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4462a3b08b77794b744d215f207e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615a83b8271b6f89469a432ee1423a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b55cc720fbe517f8ba95c7e86988bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0718c72b9677524819ce2f1a62438ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabc4ce11c65681c16a39676d29254e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4462a3b08b77794b744d215f207e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8692a851a72427d95eac78f2efd9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7426bc7343f7c515f079530f93e0c3a.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
8 . 已知集合
,x、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13d30ce87fcb597b41622df51a23933.png)
,其中
.定义
,若
,则称x与y正交.
(1)若
,写出
中与x正交的所有元素;
(2)令
,若
,证明:
为偶数;
(3)若
,且A中任意两个元素均正交,分别求出
,14时,A中最多可以有多少个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511b90f652295c5c556f8630ae5985d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13d30ce87fcb597b41622df51a23933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedc27999f4df768614e022b33b414d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b02267ebc7ed6cde9d46408c7279f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5971b046d8c65732389573ad0808c42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157967918cabbed7f5d82a291cc262f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80721f50d5063cb9f835ea6fc6870285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a6fc4d929a83295d890ac7c0c09d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22111b1f07e7873e5a156d1937eaac27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d671185c2cc9c5d88029e04f4b2ccf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec5d76db9bd05547932966c9913dc2.png)
您最近一年使用:0次
2023-02-03更新
|
662次组卷
|
5卷引用:上海市实验学校2022-2023学年高一上学期期末数学试题
上海市实验学校2022-2023学年高一上学期期末数学试题(已下线)难关必刷01集合的综合问题(3种题型30题专项训练)-【满分全攻略】(沪教版2020必修第一册)北京市广渠门中学2023-2024学年高二上学期10月月考数学试题(已下线)高一上学期期末复习【第一章 集合与常用逻辑用语】拔尖-举一反三系列(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
名校
9 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
,
,
,对任意
,定义
.若存在正整数
,使得对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
,都有
,则称集合
具有性质
.如集合
、
都具有性质
.记
是集合
中的最大值.
(1)判断集合
和集合
是否具有性质
(直接写出结论);
(2)若集合
具有性质
,求证:
和
;
(3)若集合
具有性质
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dd46e001c117104353b2e41867994e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ef42f964d02549eec898b0d3f0588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e326e8f60f19e64e32c584ccfc40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a703c80c9a9624b08ada02523257b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ff43ffdcc8b03787a1faa6509d79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff430dfb9275eed8c6e0cbe671a2798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db67bc808e5b3a6ba3f7691a50d20957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20362ac95ee78ef94caeb0579bb40bfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1baf30f84a1797c8e345c624e6cab1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10cda3e056f1db8777f3c322165bb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be13762bee8c87a904b93379c76ac8b.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d9e9e68d8fa416188fe9c5efafae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2309c5526d918b1e6d456a999ab88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e296d9adecd44ddd36ec145dcf9dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f80a1f6a8c236559e2fa55feb9ee1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923eed4cf08e8bef3e7a61ce3ba48d62.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b97c217370c2b3d22e6738006cc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d5ade4406641db15a62630f06e4201.png)
您最近一年使用:0次
2022-12-26更新
|
424次组卷
|
4卷引用:第1章 集合与逻辑 单元测试(单元重点)--高一数学同步精品课堂(沪教版2020必修第一册)
(已下线)第1章 集合与逻辑 单元测试(单元重点)--高一数学同步精品课堂(沪教版2020必修第一册)上海师范大学附属中学闵行分校2023-2024学年高一上学期期中数学试题上海市曹杨第二中学2021-2022学年高一上学期期中数学试题广西名校2024届高三高考模拟猜题试卷
名校
解题方法
10 . 已知集合
中的元素都是正整数,且
.若对任意
,且
,都有
成立,则称集合A具有性质M.
(1)判断集合
是否具有性质M;
(2)已知集合A具有性质M,求证:
;
(3)已知集合A具有性质M,求A中元素个数的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3301017a56b4427b6fab492f63b86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d13266f62539701a58bbcf895de46b1.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab146eb4208985dfe60ae3b41ba2bdd.png)
(2)已知集合A具有性质M,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ff2bdedce1d88ef6f2607f0a05c1cd.png)
(3)已知集合A具有性质M,求A中元素个数的最大值,并说明理由.
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