名校
1 . 已知A,B为集合,定义
,则下列命题中为真的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdce60669e71e09b0cce322810d21dd.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2021-08-25更新
|
1211次组卷
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5卷引用:江苏省苏州市吴中区2020-2021学年高一上学期期中数学试题
2020高一·上海·专题练习
名校
2 . 已知全集
,定义
且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a7a19832863ad25b385159bb66c539.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0f5b3af61d926dd97fde4b174226fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fa234a0dcd1d0d2e4bbefe98518012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68de235ae4924d2e66c2cba653a63c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb490920f5832b657e71d14d6a8e263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a7a19832863ad25b385159bb66c539.png)
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3 . 设
,
都是集合
的子集,如果
叫做集合
的长度,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c8ee79aa5dacae488db395591854e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5deed3f31df9c7d2e6f11c975ccc1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc686e229f88e586d639498980a9b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5572cd50ab5d8d54e2e89699ef1cfa.png)
A.集合![]() ![]() |
B.集合![]() ![]() |
C.集合![]() ![]() |
D.集合![]() ![]() |
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4 . 定义集合运算:
,设
,
,则集合
的子集的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae852867b5009e081280bf0e8a1da645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78a96152c480ec21462f47f3728ed0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f1b0858395d2424dc96616173c4b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e37e656d05244fe3a5769cd1446725.png)
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5 . (1)定义一种新的集合运算
:
.若集合
,
,设
按运算
:求集合
.
(2)设不等式
的解集为N,若
是
的必要条件,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6595597d25112f247753397d25bf5080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137976ed32d4020818ebc61d54337668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605068ffcff010dc98245aabc482ef43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be372bc439d2429a57954d85993e858d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d73a11c1c978c930290fba8c7c79f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6595597d25112f247753397d25bf5080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb6d048e00356c2f9ca7297c52a7904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca06304795e9c2c1fd0b4a52eb8d5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-10-23更新
|
389次组卷
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2卷引用:湖南省长沙市周南中学2020-2021学年高一上学期第一次月考数学试题
6 . 设集合
,集合
,若B中恰有4个元素.且定义
,则
中元素的个数是________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc51474b54120493b300a14e566cbc0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d268c0607eef881aa887ee59d368aadf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175d5ec3ea55dec0259248093f5a7702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5231cb0bfedf2f963c1830adfd74aa.png)
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7 . 设集合
满足条件,若
,则
(
且
).
(1)若
,求集合
;
(2)若
,试证明:
;
(3)集合
能否为单元素集合?为什么?
![](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/74137fa46f6f3208f5924cb1b8c66b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed961de27af72b7d11887ccfb6f15071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d59d461091895f698c5d33dcb9c804.png)
(3)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
8 . 设函数
,区间
,集合
,则使
成立的实数对
有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96af2eb3fe41db7711ae439b94e4bce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913516a99ef49e0681a522c7a7777f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c1a435e5ab8548c9f26bd11aefc4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad96b50521f4bbf3d436d05dc258083d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
A.0个 | B.1个 | C.2个 | D.无数个 |
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解题方法
9 . 设数集
,
,且集合M、N都是集合
的子集,如果把
称为非空集合
的“长度”,那么集合
的“长度”的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c5728f7a19d8e25d2b6db9d8503f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87d9f281de0a2bb7a7af59c90afdb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497401a3843497c94447c7b4002d3a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5572cd50ab5d8d54e2e89699ef1cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81919684bc4047d376c7e57dc6c8f1c.png)
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2020-10-14更新
|
618次组卷
|
6卷引用:上海市格致中学2020-2021学年高一上学期10月月考数学试题
上海市格致中学2020-2021学年高一上学期10月月考数学试题(已下线)专题05 集合与常用逻辑用语压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)上海市朱家角中学2021-2022学年高一上学期10月月考数学试题(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(沪教版2020必修第一册)(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)云南省昭通市昭阳区第一中学2023-2024学年高一下学期2月开学考试数学试题
10 . 若
是一个集合,
是一个以
的某些子集为元素的集合,且满足:
①
属于
,
属于
;
②
中任意多个元素的并集属于
;
③
中任意多个元素的交集属于
.则称
是集合
上的一个拓扑.
已知集合
,对于下面给出的四个集合
:
①
;
②
;
③
;
④
.
其中是集合
上的拓扑的集合
的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2df1bc516cf59796f7610454440afc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5c073137c7a5dc32c9376667417a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2643ed49ec598b8fd890bd92047a31.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f722bae1b9413cd8dc44c239d68c7a9.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddd2ec700917b56efe7e8cbf99dbdee.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95f0c22ffe139425acd31b909bb5ec5.png)
其中是集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
A.① | B.② | C.②③ | D.②④ |
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