1 . 向量集合
,对于任意
,以及任意
,都有
,则称
为“
类集”,现有四个命题:
①若
为“
类集”,则集合
也是“
类集”;
②若
,
都是“
类集”,则集合
也是“
类集”;
③若
都是“
类集”,则
也是“
类集”;
④若
都是“
类集”,且交集非空,则
也是“
类集”.
其中正确的命题有________ (填所有正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c0b5b15ef55baeb6e7095ce47d5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea4b13fe0b06f86baad673fa423037e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5913b03e244adcf4dec8749f9624d55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b4ea32d1f3ed0e04bcedca9f189941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148db9c7b8abbeaa814e8083bcd01c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
其中正确的命题有
您最近一年使用:0次
2020-02-29更新
|
1464次组卷
|
12卷引用:上海市华东师范大学第二附属中学2022-2023学年高二上学期开学考试数学试题
(已下线)上海市华东师范大学第二附属中学2022-2023学年高二上学期开学考试数学试题2020届上海市杨浦区高三第一次模拟(期末)数学试题2020届上海市高三高考压轴卷数学试题(已下线)专题10 集合与命题新定义-2020年高考数学母题题源全揭秘(浙江专版)(已下线)热点01 集合与逻辑-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)卷11-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)(已下线)第01讲 集合与逻辑-2(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列(已下线)压轴题平面向量与解三角形新定义题(九省联考第19题模式)练(已下线)第3章 空间向量及其应用(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)北京市中国人民大学附属中学2023-2024学年高一下学期期中练习数学试题变式题11-15(已下线)【练】专题四 与平面向量有关的新定义问题(压轴大全)
17-18高一上·上海浦东新·期中
名校
2 . 设集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ae60774f5328cb04ef69734865dc5c.png)
,如果对于
的每一个含有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
个元素的子集
,
中必有
个元素的和等于
,称正整数
为集合
的一个“相关数”
(1)当
时,判断
和
是否为集合
的“相关数”,说明理由;
(2)若
为集合
的“相关数”,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ae60774f5328cb04ef69734865dc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe872911b14948468434720e5f86f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72788b79b02ee2f81eec71afe85896c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41505e5e2ee8177abc71e367a0f9d53e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cab60ea646ffebbfd60a87d6b617fa2.png)
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16-17高一上·上海浦东新·阶段练习
名校
3 . 集合
有
个元素,设
的所有非空子集为
,每一个
中所有元素乘积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece6dcdaae3dcc2f690e08a8190cd0d8.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1270c36996f27fdff81b6d81e26f78e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d88d32b64df6bd35c5081e6144a02f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedfdfc0df673b8f8851df598a7f779f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a19d1b9e98e551f998ea32183de2d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece6dcdaae3dcc2f690e08a8190cd0d8.png)
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名校
4 . 用
表示集合
中元素的个数,设
为集合,称
有序三元组,如果集合
满足
,且
,则称有序三元组
为最小相交,由集合
的子集构成的所有有序三元组中,最小相交的有序三元组的个数是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cc01a29960cd990ae81f1c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63554db31a3246ed1e63f5e57781ea5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb8010e64b124eb2a9c3cb0d56ad1f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d614b62317dbf66e3eef15b51f89417e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63554db31a3246ed1e63f5e57781ea5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f12a019ea4cab2a4143b39043157ed.png)
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2020-01-11更新
|
532次组卷
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2卷引用:上海市浦东新区南汇中学2020-2021学年高一上学期10月月考数学试题
18-19高一上·上海浦东新·期中
名校
5 . 已知集合
,
,集合
,且集合
满足
,
.
(1)求实数
的值;
(2)对集合
,其中
,定义由
中的元素构成两个相应的集合:
,
,其中
是有序数对,集合
和
中的元素个数分别为
和
,若对任意的
,总有
,则称集合
具有性质
.
①请检验集合
与
是否具有性质
,并对其中具有性质
的集合,写出相应的集合
和
;
②试判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b6e6193c97593e74d8488e35119d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6228afd8854fbc3c1b05fcb0bfc5ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f15cabdc3d05988fd14408ee71a57f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725e7e04c2a89481457c20d6438dab0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f75ed8f6ace26756031eb3d813db6c0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692caeb314d16479c83b584c14b556bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6ea62c5decc77abe0039fb6e4fd40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2fef18cae151fadca86595209c317c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2212c2e3f325683a2f9599a1c661ff59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2cacc52ffe015e828a4a5f2fe5ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①请检验集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709a1f33195ab62f2da488b27a219c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c67b05f5f43a2d4371a42e65dea900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
②试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
6 . 对于集合
,定义函数
,对于两个集合
,定义集合
. 已知集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb41c7f5fd705222dbae9d0b37b377.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a5f27a030f42302338fb5dd947542f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf158f5e8b2b5eb06dc5432824ce95b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50803e737333db5b586113c6e11cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0893a310fb304e6a20881751806a811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb41c7f5fd705222dbae9d0b37b377.png)
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7 . 设集合
,若非空集合
同时满足①
,②
(其中
表示
中元素的个数,
表示集合
中最小元素),称集合
为
的一个好子集,
的所有好子集的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12247711394ed07a2f6a7c27f73eea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e782887fa9cd8934bc19cc1288d5f51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a462820b4535b1fa5a75c7c6e9547b.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/5d9b9765625c0a2b3a7c6850983f3400.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/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
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2019-11-08更新
|
1045次组卷
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6卷引用:上海市进才中学2019-2020学年高一上学期10月月考数学试题
上海市进才中学2019-2020学年高一上学期10月月考数学试题上海市复旦附中2019-2020学年高三上学期9月综合练习一数学试题上海市宝山区行知中学2020-2021学年高一上学期期中数学试题(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)福建省福州市闽侯县第一中学2021-2022学年高一上学期第一次月考数学试题上海市中国中学2020-2021学年高一上学期12月月考数学试题
8 . 用
表示非空集合
中元素的个数,定义
若
,且
,设实数
的所有可能取值构成集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d785b9e6898f1d203157e8ffd7771127.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecde6ad7897b29232f03521c7df3066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c645cd2caeca1d26ff0a36d4b78495ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a223d48812e9c99a1e124d1afe4384ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6335658a75a4f78c17a8c7bb108121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d785b9e6898f1d203157e8ffd7771127.png)
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2019-11-02更新
|
1404次组卷
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12卷引用:上海市华东师范大学第二附属中学2016-2017年高一上学期第一次月考数学试题
(已下线)上海市华东师范大学第二附属中学2016-2017年高一上学期第一次月考数学试题上海市川沙中学2017-2018学年高一上学期10月月考数学试题上海市建平中学2022-2023学年高一上学期开学摸底数学试题人教A版(2019) 必修第一册 必杀技 第一章 专题1集合的综合问题上海市行知中学2019-2020学年高一上学期10月月考数学试题江苏省盐城市伍佑中学2020-2021学年高一上学期第一次阶段考试数学试题上海市上海师范大学附属中学闵行分校2020-2021学年高一上学期期中数学试题上海奉贤区曙光中学2020-2021学年高一上学期10月月考数学试题上海市嘉定二中2021-2022学年高一上学期期中数学试题(已下线)期中模拟预测卷02(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)(已下线)专题1-1 集合及集合思想应用(讲+练)-2上海市杨浦高级中学2023-2024学年高一上学期期中数学试题