名校
解题方法
1 . 对于数集
,其中
,
,定义向量集
,若对任意
,存在
,使得
,则称
具有性质
.
(1)已知数集
,请写出数集
对应的向量集
,并判断
是否具有性质
(不需要证明).
(2)若
,且
具有性质
,求
的值;
(3)若
具有性质
,且
,
为常数且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7a53ccddc5210a37f12e3ab6e99df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fe482c5e20abfc9f89c876f653ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5751a1b2fb31063f3360f4ef5b0274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)已知数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c40ffb95d55e922a408458c19940dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351bb3f3c54604330fa5b6c2bc3a7502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bda892497cea43df67db57b4e2a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73eecc365f7e94267552eb430f2034e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6734531288c894a5edb143104e448ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b68031c3405c23f82fb3f352e44a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa18be2cbabe89d886b99241c4dca28.png)
您最近一年使用:0次
2 . 设集合、
为正整数集
的两个子集,
、
至少各有两个元素.对于给定的集合
,若存在满足如下条件的集合
:
①对于任意,若
,都有
;②对于任意
,若
,则
.则称集合
为集合
的“
集”.
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a4c458e37238547c09a481eb0ca295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
(2)若三元集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21edab576db2b4f56237ad687957a913.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380cc5e32580ddf29206ebb596336151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5867fde790c54e6a931c5d1d22b049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
3 . 在二维空间即平面上点的坐标可用两个有序数组
表示,在三维空间中点的坐标可用三个有序数组
表示,一般地在
维空间中点A的坐标可用n个有序数组
表示,并定义n维空间中两点
,
间的“距离”
.
(1)若
,
,求
;
(2)设集合
.元素个数为2的集合M为
的子集,且满足对于任意
,都存在唯一的
使得
,则称M为“
的优集”.证明:“
的优集”M存在,且M中两不同点的“距离”是7.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b525d8c768efd801ab58bc4c0da9221e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3957b7fdba61064a1d8990d880894678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de4e0337716e1d89eb1a6cfd7b8335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c6b5e2477070d935260db8c0f4731b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9621fabd914377b322701e2689cc912c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f111ae47bbcf70999e41743385cdc5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8eaa058fb6ca849782169fc1d94f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4d59b92bf91197446d86893fb9a0c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de67567843bcb8dc4cd20f44e1558f9c.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646e73be3272a6edfed21c3ecdc48cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b75656c76ce2e9ac0f0c213a6cbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fd7b7df5b43336d3219f16b3ce6733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f80fced6fa7e6adc72c80228443885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9591c25ee33bd1cb77bb0df04b531fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b75656c76ce2e9ac0f0c213a6cbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b75656c76ce2e9ac0f0c213a6cbe9.png)
您最近一年使用:0次
4 . 给出以下两个数学运算(符号)定义:
①若函数
,则
,其中
称为函数
的
次迭代.如:
.
②对于正整数
,若
被
除得的余数为
,则称
同余于
,记为
.如:
.
(1)若函数
,求
;
(2)设
是一个给定的正整数,函数
记集合
.
①证明:当
时,
;
②求
并猜想
.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac36cc9de2d52fa81b310df3c137559f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc5dcd0b5d4e94cb92e52ca31f0cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b956f95d6cdcded732751d6d74c14cab.png)
②对于正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ace40e2e209924905e48bf00df631f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b539bc9386988afc25da70e13ae899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706057125d5d481d23b0319e10e2d936.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e564833f8450a876460a6db43dad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91f1470cecf7c4da36644e5244775bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44a1741d645756e39740a0818412e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208bd4b35f6be79500cdf5d8e433e449.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b94f6525788e512dbc8121c49b46bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502416314c8c26f8442e639ea6a5db13.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
名校
5 . 已知有
个连续正整数元素的有限集合
(
,
),记有序数对
,若对任意
,
,
,
且
,A同时满足下列条件,则称
为
元完备数对.
条件①:
;
条件②:
.
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244a73e2cab2b626e12058164680d7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6526915197667b48dc2e6c1ff413bcf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4a8ca987823fe459fafc1c4fd057d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9458be5eac5e4b7fbd28850e43d96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba54a91d651db38d3a13a461252223e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9169084fc046cdf9b9831f4030f58217.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34affbf06b09098b13a5b89c0989fb8.png)
(1)试判断是否存在3元完备数对和4元完备数对,并说明理由;
(2)试证明不存在8元完备数对.
您最近一年使用:0次
2024-02-23更新
|
277次组卷
|
2卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期开学学业质量联合调研抽测数学试题
名校
6 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
556次组卷
|
5卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
重庆市南开中学校2023-2024学年高一上学期开学考试数学试题北京市顺义区2022-2023学年高一下学期期末质量监测数学试题(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)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
名校
7 . 设集合
,若集合S中的元素同时满足以下条件:
①
,
恰好都含有3个元素;
②
,
,
为单元素集合;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
,
是否为“优选集”;
(2)证明:若集合S为“优选集”,则
,
至多属于S中的三个集合;
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32fe32077f54b51282141c6f6217071.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296902bfc14bde752a4503d57351988a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866fcccdcf1d7bf2f73d4323b4c1c1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41e1766af890659ac91f4ed407f5a0f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7d06d943bfb67f20183899803ef150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a839a1d941f18f084505c7e8614c984b.png)
(2)证明:若集合S为“优选集”,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7060f36f24efe532ddd3f12084f36d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
您最近一年使用:0次
2023-01-19更新
|
566次组卷
|
4卷引用:重庆市南开中学校2023-2024学年高一上学期九月测试数学试题
重庆市南开中学校2023-2024学年高一上学期九月测试数学试题北京交通大学附属中学2021-2022学年高一上学期期中数学试题河南省周口市周口恒大中学2023-2024学年高一上学期9月月考数学试题(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)
8 . 对于任意的
,记集合
,
,若集合A满足下列条件:①
;②
,且
,不存在
,使
,则称A具有性质Ω.如当
时,
,
,
,且
,不存在
,使
,所以
具有性质Ω.
(1)写出集合
,
中的元素个数,并判断
是否具有性质Ω.
(2)证明:不存在A、B具有性质Ω,且
,使
.
(3)若存在A、B具有性质Ω,且
,使
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6136140ae3eda80fa2251dd6f3840415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d61ab4e28840d2597566a9677cf1670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8a4824db78a0f34777372e4cb7ff9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac5230b93cc884fe3b8798d0cd2f30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b354b577ec9cdb8941ba4f7b66a8aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba1217bdce7fed00b4c488ae2d1c83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1922efd1e913d2721fbf240ea3740ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d64a4f7b1f0fb56b37f75d95a50d321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b354b577ec9cdb8941ba4f7b66a8aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)证明:不存在A、B具有性质Ω,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef35a92301f139a035fc643ff1545c1.png)
(3)若存在A、B具有性质Ω,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a347c4b63fad850a75f36e87f44c86.png)
您最近一年使用:0次
2022-04-09更新
|
755次组卷
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5卷引用:重庆市南开中学高2022-2023学年高一上学期第一次月考数学试题
重庆市南开中学高2022-2023学年高一上学期第一次月考数学试题北京市清华大学附属中学朝阳学校2021-2022学年高一3月质量检测数学试题(已下线)1.3 交集、并集(2)(已下线)第02讲 集合的运算(7大考点13种解题方法)-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)高一上学期期中考试解答题压轴题50题专练-举一反三系列
名校
9 . 设集合
,集合
,如果对于任意元素
,都有
或
,则称集合
为
的自邻集.记
为集合
的所有自邻集中最大元素为
的集合的个数.
(1)直接判断集合
和
是否为
的自邻集;
(2)比较
和
的大小,并说明理由;
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbad957385c90ca3a76e717e4b4e7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cd2449f6ae27a72287be95a661d8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320a7c616f6f7207a0a38bb707ac2205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbcd3d6b77c949be81a946ac9ed9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73707750f88b56101446fce394e0faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7f71b0119f257edb8d5060a810de92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)直接判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4047b80385ef60ea5e9a1f184e7b948b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecde0085a473948c061942a1728a37c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64927a98d33b49dc5c6a0e65e5e8eb53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41788e238eff245e567b58dea3a0003.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f4f09e879e859a946b2d5e2d844342.png)
您最近一年使用:0次
2021-07-15更新
|
896次组卷
|
7卷引用:重庆市万州第二高级中学2023-2024学年高一上学期10月月考数学试题
重庆市万州第二高级中学2023-2024学年高一上学期10月月考数学试题 北京市八一学校2020-2021学年高一下学期期末数学试题(已下线)1.2 集合间的基本关系-2021-2022学年高一数学尖子生同步培优题典(人教A版2019必修第一册)(已下线)期末重难点突破专题01-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)(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)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)专题01 集合与常用逻辑用语3-寒假作业单元合订本
名校
解题方法
10 . 设集合
,且S中至少有两个元素,若集合T满足以下三个条件:①
,且T中至少有两个元素;②对于任意
,当
,都有
;③对于任意
,若
,则
;则称集合
为集合
的“耦合集”.
(1)若集合
,求集合
的“耦合集”
;
(2)若集合
存在“耦合集”
,集合
,且
,求证:对于任意
,有
;
(3)设集合
,且
,求集合S的“耦合集”T中元素的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b94a0abdcc3807bf392db9ff45b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eee24115b5913c454fe5a93f176db80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7741c8d8f0486556a102d904fb26a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8339eab9c659e50db86828b65f825e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566d386cbedb1c8750f4837633c2af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0086b15b30b83d428b35cdbe094810f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5718e9c8baa106b447f9fae23e730de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a8b2c7049b225429ace45c69a44d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a09b275c36edd90e33b7dbd4d8a1ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799794fea82a353250cb5d27a30002cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499f74ed37d11fb9d30d9ee10c337c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b19fb48a58c310c0432c93e054c26ff.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e91972c88f7dcf857a74fdbd57deb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa09412f1c12451c54596ce4d58fffa.png)
您最近一年使用:0次
2021-01-27更新
|
1319次组卷
|
5卷引用:重庆市璧山中学校2021-2022学年高一上学期10月月考数学试题