名校
1 . 已知自然数集
,非空集合
.若集合E满足:对任意
,存在
,使得
,称集合E为集合A的一组m元基底.
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
;
②
.
(2)若集合E是集合A的一组m元基底,证明:
;
(3)若集合E为集合
的一组m元基底,求m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaa2be7b1653f2371891e9a794f023d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5002b44e87e59f1e1fda6a841de5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c059a6234c274a3aa626b20698263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53613f4c8d697ad45bd08f29ef76f19e.png)
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93b026b2bd1f754bcee49e48c6bbb4.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3210812ece496c3ab3396e9ec2f0c6e.png)
(2)若集合E是集合A的一组m元基底,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e41403eba28ee0f497c79953b842ca1.png)
(3)若集合E为集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1341ae10a275cd370eb014d0f505f3.png)
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2023-11-03更新
|
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2卷引用:北京市人大附中2023-2024学年高二上学期期中数学试题
2 . 已知集合
,
表示集合
中的元素个数,当集合
的子集
满足
时,称
为集合
的二元子集. 若对集合
的任意
个不同的二元子集
,均存在对应的集合
满足:①
;②
;③
,则称集合
具有性质
.
(1)当
时,若集合
具有性质
,请直接写出集合
的所有二元子集以及
的一个取值;
(2)当
时,判断集合
是否具有性质
?并说明理由;
(3)当
时,若集合
具有性质
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42eb7811b73b96e79306c3c4ffd4467a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.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/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a50d86b46e0771672997f4ec429e91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aabc1d4d773a0d1fb49fae1aeff9308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a01cb028fb377008e680de7231c72e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3b2543aae6153dd76db856b45e9f50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39373b4ce5129d616cc1980c7ba5363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556e66db5f43a62380c2e77caf88cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
3 . 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
|
658次组卷
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5卷引用: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
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)(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
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)
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2022-11-17更新
|
626次组卷
|
7卷引用: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
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)(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)(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)
5 . 已知集合
(
)具有性质P:对任意的
(
),
与
两数中至少有一个属于A.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)证明:
,且
;
(3)当n=5时,若
,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657becc77ba5ea1f2f83dac2db8f5d51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcf01e3d8479c75e2c48037509a32b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460eeeb21bb7aee40a910f6c90b85e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b5de1e43419f74ef5a46c509ac44f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21adcc8de899f08f68ab04b704acc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1d26a5065efbd0900540557f06e5a6.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d3502efe17d2c399d3ef319c81b1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963e992724b7092e28d185967d16560c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7970494edfaba8f53f570c0ebc6cc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84429aff3a96fd3ec544cad66d4bf29c.png)
(3)当n=5时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f83381978ab0c8f4714bab33c875dd.png)
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2022-10-15更新
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384次组卷
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2卷引用:北京市朝阳区东北师范大学附属中学朝阳学校2023-2024学年高二上学期期中学习质量监测与反馈数学试卷
名校
6 . 设A是非空数集,若对任意
,都有
,则称A具有性质P.给出以下命题:
①若A具有性质P,则A可以是有限集;
②若
具有性质P,且
,则
具有性质P;
③若
具有性质P,则
具有性质P;
④若A具有性质P,且
,则
不具有性质P.
其中所有真命题的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6493575a2d595bebd8e813c3d79fb8c.png)
①若A具有性质P,则A可以是有限集;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8543bb9be52b25cf5be0a39110c9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
④若A具有性质P,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62bc98b651b58ecbc295ef67aa1c42a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3516cead1976248defbf1ffe368170.png)
其中所有真命题的序号是
您最近一年使用:0次
2021-04-07更新
|
2421次组卷
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8卷引用:北京市东直门中学2020-2021学年高二下学期期中数学试题
北京市东直门中学2020-2021学年高二下学期期中数学试题北京市东城区2021届高三一模数学试题北京市海淀区一零一中学2022-2023学年高一上学期数学统练试题(一)北京市朝阳区人大附中朝阳分校2022-2023学年高一上学期9月月考数学统练试题(1)北京市东直门中学2022-2023学年高一上学期9月月考数学试题北京市首都师范大学附属中学2022-2023学年高一上学期10月月考数学试题(已下线)第一章 集合与常用逻辑用语(B卷)-2021-2022学年高中数学必修第一册课时解读与训练(人教A版2019)(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)
名校
7 . 已知集合
,
,
,
,其中
.定义
,若
,则称
与
正交.
(1)若
,写出
中与
正交的所有元素;
(2)令
若
,证明:
为偶数;
(3)若
且
中任意两个元素均正交,分别求出
时,
中最多可以有多少个元素.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0a422a1f3b4197761a32eea75e5f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/984c76feb97fd60961042a5a0490042e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4d0cff6698ac42bb2158babd15b20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7cf6c3ef21af43bd1b4b9ce9ad5721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c015c9a3f30d0be75666375733ea35cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2e64804787fb0b18a3d8eee3570578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157967918cabbed7f5d82a291cc262f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80721f50d5063cb9f835ea6fc6870285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27db54d88c391992ad9cbc65ef509e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67aadad8f385811fd0d0c8541007cbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2020-11-15更新
|
795次组卷
|
3卷引用:北京市海淀区教师进修学校附属实验学校2020-2021学年高二上学期期中数学试题
8 . 已知集合
,且
中的元素个数
大于等于5.若集合
中存在四个不同的元素
,使得
,则称集合
是“关联的”,并称集合
是集合
的“关联子集”;若集合
不存在“关联子集”,则称集合
是“独立的”.
分别判断集合
和集合
是“关联的”还是“独立的”?若是“关联的”,写出其所有 的关联子集;
已知集合
是“关联的”,且任取集合
,总存在
的关联子集
,使得
.若
,求证:
是等差数列;
集合
是“独立的”,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cdcb0e77b3ae3e701c6b51e15e2346.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f1c94368c3a41177ff42cfedc0eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e0ad51c5541ec3dcca4a9845f8b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8021f4f4c253a00360bf8f9425610e1.png)
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2020-02-09更新
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1547次组卷
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10卷引用:北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题
北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题北京市第五十七中学2021-2022学年高二下学期期末考试数学试题北京市日坛中学2023-2024学年高二下学期第三次月考(6月)数学试卷2020届北京市海淀区高三上学期期中数学试题(已下线)专题02 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)北京市海淀区2021届高三模拟试题(一)北京市第八中学2023届高三上学期12月测试数学试题北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮上海市上海中学2022届高三下学期高考模拟3数学试题
名校
9 . 已知关于
的方程
有2个不相等的实数根,则
的取值范围是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac15eba07325d86807fc901db338e504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-07-05更新
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4卷引用:北京交通大学附属中学2021-2022学年高二下学期期中练习数学试题
名校
10 . 设n 为不小于3的正整数,集合
,对于集合
中的任意元素
,
记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3225ca41c60a7218ca767f040d6572b.png)
(Ⅰ)当
时,若
,请写出满足
的所有元素![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3217fa687c8a339e86fc482c826e2edf.png)
(Ⅱ)设
且
,求
的最大值和最小值;
(Ⅲ)设S是
的子集,且满足:对于S中的任意两个不同元素
,有
成立,求集合S中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a30bb28b4ae1de6653b19b86c6a62e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708b9404e9fc4bf4b59fcd9602eb9365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4f902ad4b1c9f680f077d554ac8dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd08690fdd2e5c3adceb6e34c27a7b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3225ca41c60a7218ca767f040d6572b.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea7c1dda52682bd8916a23a6c6a5f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a16f753d267623f662217e95512686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e44c4716a87d56ea5049c4b519f8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3217fa687c8a339e86fc482c826e2edf.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebd52238f0609dace63a6dc510d3161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980b0bc606fb6b9927381323dce364c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8356f6284bf7013c4b96c16d7738df9.png)
(Ⅲ)设S是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708b9404e9fc4bf4b59fcd9602eb9365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24793085828ff3185538dc2ca5fdaf22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ddfac61514572bdea24f7dedc15d53.png)
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2019-01-24更新
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3卷引用:北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题