1 . 已知集合
,设A是S的至少含有两个元素的子集,对于A中的任意两个不同的元素
,若
都不能整除
,则称集合A是S的“好子集”.
(1)分别判断数集
与
是否是集合S的“好子集”,并说明理由;
(2)证明:若A是S的“好子集”,则对于A中的任意两个不同的元素x,
,都有
;
(3)求集合S的“好子集”A所含元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54730b349603779705381ecfaa3d114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7f07dd4a224f90b28ca7d711e3efdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef27cd09f4ecc055fd7e72b3b368e5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91edb18f49d6acc68a3d8d1a1be6a5b.png)
(2)证明:若A是S的“好子集”,则对于A中的任意两个不同的元素x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddc8b4ed2041296890090da616d49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4be7ed8ae7440b7b7efae8889cc510.png)
(3)求集合S的“好子集”A所含元素个数的最大值.
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2 . 对于给定的整数
,若非空集合
满足如下条件:①
;②
;③对任意
、
,若
,则
,则称集合
为“减
集”.
(1)分别判断集合
是否为“减0集”或“减1集”,并说明理由;
(2)证明:不存在“减2集”;
(3)请写出所有的“减1集”.(无需说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5413749128ae964686121c1db13e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebabd7323bae39388835a33e09046c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7106b876fcce8d7f2663e5aa2b982f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a9edd24f30a64e24fbe08992e2927f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9f6c43a9072ed4df8ad37370468a9c.png)
(2)证明:不存在“减2集”;
(3)请写出所有的“减1集”.(无需说明理由)
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3 . 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)
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4 . 对于任意有限集
,定义集合
表示
的元素个数.已知集合
为实数集
的非空有限子集,设集合
.
(1)若
,求集合
和
;
(2)已知
为有限集,若
,证明:
.
(3)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185f1dec719b499d236ee7accaed0907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c7673f4ca064bb1097f95523bf47cc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab403f48a374c87fefc0c24923a063a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9281c61411eceeecf11c1f6ac31c2eec.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eccd49c9b9e3663880dac5b3029972a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2198afa66c6a0cf4bb1698884da212.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09231ce23847f1780d130475ee341c96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ddc772b27a6a72d3d6295f75e21298.png)
您最近一年使用:0次
2022-11-11更新
|
493次组卷
|
5卷引用:期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)
(已下线)期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)上海市行知中学2022-2023学年高一上学期期中数学试题(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(人教A版2019必修第一册)(已下线)期中真题必刷压轴60题(15个考点专练)-【满分全攻略】(人教A版2019必修第一册)北京市陈经纶中学2022-2023学年高一上学期12月诊断数学试题
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5 . 对于一个数集
,若满足下列条件:①
中至少有两个非零元素;②
;③任取
中的两个非零元素,它们加、减、乘、除后的结果都仍属于
,则称数集
为数域,如有理数集
为有理数域,实数集
为实数域.
(1)证明整数集
不是数域;
(2)判断集合
是否为数域,并说明理由;
(3)若
为任意两个数域且
中至少存在两个非零元素,判断
是否为数域,并说明理由.
![](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/ca05074e5a317ae45d073962bdf74dbe.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/316ecb1589c3cc179e2f62507020771e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)证明整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0ecd416d6dc3d886b7bf73fc285dde.png)
(2)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddf63bde6be124c5037dee2130770ff.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0899a23c018a1f574b02688c23529d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98119b025fefb8e997e2432d4e10d9cb.png)
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6 . 对于给定集合
,若集合
中任意两个不同元素之和仍是集合
中的元素,则称集合
是“封闭集合”.设
为实常数且
,集合
,证明:集合
为“封闭集合”的充要条件是:存在整数
,使得
.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01addf1c0dae299be04495dec2a3c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a141495f9abd68126822a2ae920aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd44d872abf0e0480c139e86d9bb5c1.png)
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7 . 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)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8d9e00ef22cd220a6bbd291f280a83.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)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293bd318a7a3796d3589db25148be688.png)
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解题方法
8 . 设
为非空集合,定义
(其中
表示有序对),称
的任意非空子集
为
上的一个关系.例如
时,
与
都是
上的关系.设
为非空集合
上的关系.给出如下定义:①(自反性)若对任意
,有
,则称
在
上是自反的;②(对称性)若对任意
,有
,则称
在
上是对称的;③(传递性)若对任意
,有
,则称
在
上是传递的.如果
上关系
同时满足上述3条性质,则称
为
上的等价关系.任给集合
,定义
为
.
(1)若
,问:
上关系有多少个?
上等价关系有多少个?(不必说明理由)
(2)若集合
有
个元素
,
的非空子集
两两交集为空集,且
,求证:
为
上的等价关系.
(3)若集合
有
个元素
,问:对
上的任意等价关系
,是否存在
的非空子集
,其中任意两个交集为空集,且
,使得
?请判断并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5993d7b820c0b182711674de0d85a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978ef4aebb02ab0320e8ff61d7195392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba8172b545998849067b299ac4949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddf512fd22bcd30c39da2a8ef41a82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd8717bdcfbc527676ae2a80285881e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7d20713240ffa343a7b7b8da43c577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532da63ac3aa945328904b9db8b05bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928008f619c199d9375b03b63f17f0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248bff56f76fc98ac9e16b2c751bc142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/256b72e8048ad33ee1f6919b04b70ab7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若集合
![](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/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](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/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.png)
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名校
9 . 对于任意有限集S,T,定义集合
,
表示S的元素个数.已知集合A,B为实数集R的非空有限子集,设集合
.
(1)若
,求集合C及其元素个数
;
(2)若
,求
的值;
(3)已知D为有限集,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c2770eb8c85bdc511221637c16e0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44307573cc59d670ca1f6d02593b83f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3518dc47ae1c0534092ca302a730472e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed1774cd6b193026d3391cefa689310.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c0a712c58633fb214b1c405efe992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5901b6ae6466abfd6c323bdeeadd6c99.png)
(3)已知D为有限集,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680d51970e92b92342223af8b37d4a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05ed8035ddd31bc242af5a52e9e8a08.png)
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2022-09-06更新
|
483次组卷
|
5卷引用:期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)
(已下线)期中真题必刷压轴30题-【满分全攻略】(沪教版2020必修第一册)上海市建平中学2021-2022学年高一上学期期中数学试题(已下线)上海高一上学期期中【压轴42题专练】(2)新疆乌鲁木齐天山区2023-2024学年高一上学期第一次阶段性测试数学试题(一)(已下线)高一上学期期中【压轴60题考点专练】(必修一前三章)-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)
22-23高一上·上海浦东新·阶段练习
名校
10 . 已知M是满足下列条件的集合:①
,
;②若
、
,则
;③若
且
,则
.
(1)判断
是否正确,说明理由;
(2)证明:“若
,则
”是真命题;
(3)证明:若
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca05074e5a317ae45d073962bdf74dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fefe237385a2dc1b005d8dc61ef56eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580ce638933a1c81da5e2e1b656c77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c443466385f21cd3f06e2e4229add79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de68508dc0a95fc4b5de772390260db.png)
(2)证明:“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79d04bf7882fd278b9ba53b791c156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580ce638933a1c81da5e2e1b656c77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f06a4a9deb51418c20e7e7376cc807.png)
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