1 . 若集合
,其中
为非空集合,
,则称集合
为集合A的一个n划分.
(1)写出集合
的所有不同的2划分;
(2)设
为有理数集Q的一个2划分,且满足对任意
,任意
,都有
.则下列四种情况哪些可能成立,哪些不可能成立?可能成立的情况请举出一个例子,不能成立的情况请说明理由;
①
中的元素存在最大值,
中的元素不存在最小值;
②
中的元素不存在最大值,
中的元素存在最小值;
③
中的元素不存在最大值,
中的元素不存在最小值;
④
中的元素存在最大值,
中的元素存在最小值.
(3)设集合
,对于集合A的任意一个3划分
,证明:存在
,存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e887bc41e7c72b69482b7cb153b9f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c7bb3662baf8ab4da46099adc0180a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c5b1cefd28f020a899803181867be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a111d44296a6d4c373e33e0267baeb8.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b064529d4274a25ea70cec901689595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c303b55101c9d049947443d85bd3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b31852ebf26c81693dc084facc76a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a99ef56247036a98e53aa8c16c3e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48ec13d90542aaca7af71224a3d8ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2199afe5dd5ad25962537abfa209b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f351ce8d2e5f2160bf2f771642f6dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92916a0ce7c44bbd09a54a9aedd2e8ac.png)
您最近一年使用:0次
2022-07-08更新
|
1219次组卷
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6卷引用:北京市第一七一中学2023-2024学年高一上学期12月调研数学试题
北京市第一七一中学2023-2024学年高一上学期12月调研数学试题北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题(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)(已下线)高一上学期期末【压轴60题考点专练】-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)北京市海淀区首都师范大学附属中学2023-2024学年高一上学期10月期中练习数学试题(已下线)第1章 集合与常用逻辑用语-【优化数学】单元测试能力卷(人教B版2019)
名校
2 . 设集合
为非空数集,定义
.
(1)若集合
,直接写出集合
及
;
(2)若集合
且
,求证
;
(3)若集合
且
,求
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e32ae0e537ab483485e3dc6628b2f3a.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce46889ee6889ca41c5bd19eaf0e242f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4d331fa6921e8ebc0b1fc4affd22ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
3 . 设
,记
,若
,
,则称A为
中的一个移位集,
为A的一个移位数.记A中的元素个数为|
.
(1)判断下列集合是否是
中的移位集.若是,求出相对应的移位数.
①
,
②
;
(2)若
中所有满足
的集合A都是移位集,求m的最大值;
(3)对任意满足
的集合A都是
中的移位集,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b8b0bc774a1a88cea41abb4e47e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b938a9b748bf1590ea5a6652669643c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d5fa78bfaa823a1d09ab57208532d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2fc2224e26690053448db851fbcbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4978089eb165d2241a35275396794d06.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48e81b54f78b96294295542b010dfb.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b89a8282cafe1769891b39ec8c0102.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f255c4c9acc49c187ab5990228480c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df91ed9bc04acc7b2edb6b522b953efb.png)
(3)对任意满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500aee7a5f2fa5c8cfc6f55b66546024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2021-10-27更新
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1037次组卷
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4卷引用:黑龙江省哈尔滨市第三中学2021-2022学年高一上学期第一次验收考试数学试题
黑龙江省哈尔滨市第三中学2021-2022学年高一上学期第一次验收考试数学试题江西省吉安市第三中学2021-2022学年高二10月第一次段考数学(理)试题(已下线)突破1.3集合的基本运算(重难点突破)(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
4 . 对正整数
,记
,
.
(1)用列举法表示集合
;
(2)求集合
中元素的个数;
(3)若
的子集
中任意两个元素之和不是整数的平方,则称
为“稀疏集”.证明:存在
使得
能分成两个不相交的稀疏集的并集,且
的最大值为14.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477ac10cc039be2d2a06fad831fa523f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d7155d7bd00e29d2e9324a8845735b.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb82d62ae6889a177c70d3adf8a91056.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2021-10-17更新
|
956次组卷
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6卷引用:上海市大同中学2021-2022学年高一上学期10月月考数学试题
上海市大同中学2021-2022学年高一上学期10月月考数学试题(已下线)1.1 集合的运算(第4课时)上海市青浦高级中学2022-2023学年高一上学期期中数学试题(已下线)第1章 集合与逻辑(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(沪教版2020必修第一册)湖南省岳阳市2022-2023学年高一下学期期中数学试题(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)
5 . 已知
表示不小于
的最小整数,例如
.
(1)设
,
,若
,求实数
的取值范围;
(2)设
,
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d45335f199dd5cf7e6a983a4110ead.png)
上的值域为
,集合
中元素的个数为
,求证:
;
(3)设
(
),
,若对于
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d60d72b51085ff7074db4052a867df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28a3002b619eb45f43ddd7f80af1d62.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3649d731e13efb44ebcd880f5fe45491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838b7964f9253718937399d087b061ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f86cbe53a0d1c57ec6875c3bda0224e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d45335f199dd5cf7e6a983a4110ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eb761dbf1a5a1106dad1a25ce08a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a940fb552e971bc2d56920ab1931704c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93086b41db64fef24e09e0ca5fac715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f04a01f96738e961084100ed412722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057f214e6d3bd8beb020c7a667d97811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e8f7120bfaf3ff3a6c5564ed826769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-02更新
|
781次组卷
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2卷引用:上海市十三校2016届高三下学期3月联考(理)数学试题
解题方法
6 . 已知函数
和
,定义集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
,
,若
,求m的取值范围.
(2)设
,
,
,若
,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e204b1d7ee9fec55811da546bd2d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f220ef5339248b2971cecebb6a92294b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bac659eca0067a8f5217d0ce62c2c0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6436413dff637d3ae243f82bd22c4f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bbf9858659de45bd26111af7babef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6d4b11a69708e588e4bbac9f2b3f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbf3b0349dc38eb54864384c6ef043e.png)
您最近一年使用:0次
名校
7 . 在直角坐标平面
中,已知两定点
与
位于动直线
的同侧,设集合
点
与点
到直线
的距离之差等于
,
,记
,
.则由
中的所有点所组成的图形的面积是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a82b85d3f59cf6c73fd6f31cb8bd097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f10508c6baf6ddeee4c831ed691b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94104b402db1cecee26cb88883f8d46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d620d0c8f548ad59124b8ef4a3f1ad64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcc00afb7300416974b0527d1db17eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12b6bd56bfaad4d9034068f39335e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724a99af51ca6d12e9cef3192081e3a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d4dcda034c1e106aca4d1706c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7e1a423449139ad35947c47e2effd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2017-07-01更新
|
1014次组卷
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4卷引用:上海市华东师范大学第二附属中学2021-2022学年高二上学期12月月考数学试题
(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期12月月考数学试题上海市金山中学2016-2017学年高二下学期期末考试数学试题(已下线)专题4.1 坐标平面上的直线【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市南洋模范中学2023-2024学年高二下学期期中考试数学试卷