1 . 若平面点集
满足:任意点
,存在
,都有
,则称该点集
是“
阶稳定”点集.现有四个命题:
①对任意平面点集
,都存在正数
,使得
是“
阶稳定”点集;
②若
,则
是“
阶稳定”点集;
③若
,则
是“
阶稳定”点集;
④若
是“
阶稳定”点集,则
的取值范围是
.
其中正确命题的序号为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46555735dde9e57ac52e1eeb687f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38e916d4c713366616379768222c5da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd29dc9d11ca26bc64a31b344da89a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
①对任意平面点集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6d5b3bdd2b277ed94306cca2a39e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24688a4ab2e909d1002685bb68d7cb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d59834cd0f5a9e7911c313c431c1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b319d1866ba76cba6a91f09f610f50.png)
其中正确命题的序号为
A.①② | B.②③ | C.①④ | D.③④ |
您最近一年使用:0次
2020·全国·模拟预测
2 . 设
是一个非空集合,集合
是集合
的若干个子集所组成的新集合,即
且
,其中
表示集合
中元素的个数,若满足:
(1)
,
;
(2)对于
中的任意两个元素
,
,其交集
;
(3)对于
中的任意两个元素
,
,其并集
;
则称
是集合
上的一个拓扑结构.则下列说法正确的是________ .(写出所有正确说法的序号)
①集合
是集合
上的一个拓扑结构;
②集合
是集合
上的一个拓扑结构;
③集合
是集合
上的一个拓扑结构;
④集合
上仅有3个拓扑结构且分别为
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57178ca59ce636b842c01522e27f63cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5608a4053306006d628cb0be066f7082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c1a314e85f1da82472ee3cc086c8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2afc0935375c7cf0308b51cec471391.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07518e2599d50a7d2424b064be016ee4.png)
(3)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22bb9cb63710b690db1a953a0c7bd664.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419af69356218a1034bb00adc08903f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86a10eaa25bea651fea8bb8427c4a12.png)
②集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5db65e04cdc1fd4993e6327f049da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86a10eaa25bea651fea8bb8427c4a12.png)
③集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe24ffeb1a13a941ef91bd5aa43e7195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
④集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298385ae5d53312a7d92be9f87c50e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828436db0e62cee14917c51697e67fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6addb4806cd1dd3ae0fb8dc7bed566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fecf241ac33196d497ad8fec84fb9c4.png)
您最近一年使用:0次
名校
解题方法
3 . 已知下列四个说法中:
①
与
表示同一函数;
②已知函数
的定义域为
,则
的定义域为
;
③不等式
对于
恒成立,则
的取值范围是
;
④对于集合
,
,
若
,则
的取值范围
,其中正确说法的序号是______ .
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b3e897dea11f9b673c1ad2d5878bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9727cca4ae89db26bfa2f8b2bb76c8c4.png)
②已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b1af5d4b930f8989cf63d44768621e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8dd34d6699daf6eae648c1fae51789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4fd84394e897ebf6c4814b841d427b.png)
③不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e2166990a5abe6f719ddc44580d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3213a7a72b5e376ee25efd535398fb7d.png)
④对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59df66e355dfa724058cd975240e5f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac3ecd5d06ab40ec3f071ea185f7e75.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0f0162009195038650a6ccea57352e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3bbd954f890ec2a777fa411c4c313fd.png)
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4 . 设
为实数集
的非空子集.若对任意
,都有
,则称
为封闭集,下列说法:
①集合
为封闭集;
②若
为封闭集,则一定有
;
③封闭集一定有无数多个元素;
④若
为封闭集,则满足
的任意集合
也是封闭集.
其中的正确的说法是_____ (写出所有正确说法的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced3ae86527d84d5cfc6f78eaa33de24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ffd656c582297212ed47fe834fe92f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1330666c9b3d23a6fd9b25380270a1a9.png)
③封闭集一定有无数多个元素;
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b72ac53610811542292a730a8a0079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
其中的正确的说法是
您最近一年使用:0次
2018-01-10更新
|
659次组卷
|
4卷引用:2012届山东省淄博一中高三教学质量检测(四)文科数学试卷
(已下线)2012届山东省淄博一中高三教学质量检测(四)文科数学试卷2018届高三数学训练题(1 ):集合的关系与运算 【全国百强校】广西南宁市第三中学2018-2019学年高一上学期第一次月考数学试题人教B版(2019) 必修第一册 过关斩将 第一章 专题强化练2 集合中的“新定义”问题
5 . 定义全集
的子集
的特征函数为
,这里
表示
在全集
中的补集,那么对于集合
,下列所有正确说法的序号是 .
(1)![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/e1a03c722e254e899ed8bb72bbae1438.png?resizew=160)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfadfb8c7b48eba6539b2be8f5e43f14.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30caa01d6b04ad5c3664b231e67bf97a.png)
(4)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/58df1002603247b69d980ddd94018215.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/aa7bd075a8904a51825641b63287e6f8.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/27b18d3abb1f40e4b8a9c01b6b1f6889.png?resizew=131)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/84995a2cc6e34eaeab517617d0e860cc.png?resizew=35)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/aa7bd075a8904a51825641b63287e6f8.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/58df1002603247b69d980ddd94018215.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/12406e6bca9643958640e1170d70ea11.png?resizew=73)
(1)
![](https://img.xkw.com/dksih/QBM/2015/5/18/1572112270327808/1572112276037632/STEM/e1a03c722e254e899ed8bb72bbae1438.png?resizew=160)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfadfb8c7b48eba6539b2be8f5e43f14.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30caa01d6b04ad5c3664b231e67bf97a.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c212d9f8d29eceee59848ed41d9c6dda.png)
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