1 . 已知集合
,对于
,
,定义
与
之间的距离为
.
(1)已知
,写出所有的
,使得
;
(2)已知
,若
,并且
,求
的最大值;
(3)设集合
中有
个元素,若
中任意两个元素间的距离的最小值为
,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a1ddf7f51f115fa436aadb2de92b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e6a5b4c75edf2ee68f935b2e3fe12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1a7c3713945abc4eca8485945abf32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab4a9bfa50054c808dd8190305d0abd.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e25cf1d30f458593f08325f85f6e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c72cbaca91d8e578762c4f0b6750a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4aaf68eac26dd95e0eb726913dfc17b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003fbb029cdb6d5d7f93e29dca371f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c332b53365518c5cf5361bf3cacd47b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11feb79d33ca429733a82c5d88393ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d528f49ab8d7fd971c5bb8fa7f24d4.png)
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名校
2 . 已知集合
(
,
),若存在数阵
满足:
①
;
②
.
则称集合
为“好集合”,并称数阵
为
的一个“好数阵”.
(1)已知数阵
是
的一个“好数阵”,试写出
,
,
,
的值;
(2)若集合
为“好集合”,证明:集合
的“好数阵”必有偶数个;
(3)判断
是否为“好集合”.若是,求出满足条件
的所有“好数阵”;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7c07bd06408ada63e19cd38444a8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5790497e607490f8d6c184f11ad260.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f799bc4317846951767f4aa196bfc105.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54946204c502727ffaee3c0172d195a3.png)
则称集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(1)已知数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93838d1ac2b07386b69165fe00d9e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
![](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/595044a7750ab4f84519041979c3d780.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1acb90636d27c85b45c0204035594f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c95469d8d40311c876b3724f032d7e.png)
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2024-03-27更新
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1032次组卷
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4卷引用:北京市第八十中学2023-2024学年高二下学期期中考试数学试题
北京市第八十中学2023-2024学年高二下学期期中考试数学试题北京市丰台区2023-2024学年高三下学期综合练习(一)数学试题北京市日坛中学2023-2024学年高一下学期期中考试数学试题(已下线)压轴题01集合新定义、函数与导数13题型汇总 -1
名校
3 . 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
4 . 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)
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名校
5 . 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
|
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
6 . 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
|
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)
7 . 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)
您最近一年使用:0次
2022-10-15更新
|
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
8 . 若函数
满足:对于
,都有
,且
,则称函数
为“
函数”
(1)试判断函数
与
是否为“
函数”,并说明理由
(2)设函数
为“
函数”,且存在
,使
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82754353d23aaa9a5fd2437c31e872d6.png)
(3)试写出一个“
函数”,满足
,且使集合
中元素最少(只需写出你的结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abed7edbae224272e56661384ac4a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e333588299e2ff881262526504ad94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bf49c91a6d010c4cefcddcca4d0e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec585cec335e338b14fc7b8edf599585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f9b18683b347a6034ac25994499a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79ff54854a125d1ea64651c4af512f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5140af075af23abc35a5974d5c1a4dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82754353d23aaa9a5fd2437c31e872d6.png)
(3)试写出一个“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290640a1de8c750df33141d1544a4409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b6ea94669997d0716dff9ce0025b2a.png)
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名校
9 . 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
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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
10 . 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
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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