解题方法
1 . 设全集
,集合A是U的真子集.设正整数
,若集合A满足如下三个性质,则称A为U的
子集:
①
;
②
,若
,则
;
③
,若
,则
.
(1)当
时,判断
是否为U的
子集,说明理由;
(2)当
时,若A为U的
子集,求证:
;
(3)当
时,若A为U的
子集,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fefd9d7303a04708b4f2d728e78361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed0c7122ffdbf145d72a310671465fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0412e8d25fa4748e3f6784611bd61990.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8a1b0b32229f6a9f5b85c11f05bee2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658f2824532e5b72962fe34a22c27c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251a5b0faec4a29eff8173a633c0b765.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea9f77724293f232a0578b283a9870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8489b7692d3889aede2335c3ac8aca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb76e516509e33dc0d29663cc6b884bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd131b82e404452880d7a97792f22493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7844925f9077aa32c990fc20a51467.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcd23a8020d731bd512bb8df45ea594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e13bbde03ffad05ecc3fee8120b6a6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575c2057865186fb80a50f67ee6ea70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0acc53fa720475ae4c2ed59691fce0.png)
您最近一年使用:0次
2023-01-06更新
|
882次组卷
|
10卷引用:北京市朝阳区2022-2023学年高一上学期数学期末试题
北京市朝阳区2022-2023学年高一上学期数学期末试题北京市第五十七中学2022-2023学年高一(1+3科技创新试验班)下学期期中考试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列(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03集合的运算-【倍速学习法】(人教A版2019必修第一册)(已下线)第一章 集合与常用逻辑用语(单元提升卷)-【满分全攻略】(人教A版2019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)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列(已下线)FHsx1225yl138
名校
2 . 已知集合
是集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17827b180be7fe6257a170ac4f14ba0e.png)
的一个含有
个元素的子集.
(Ⅰ)当
时,
设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e935b5d0182c2382de28c46cb968af3.png)
(i)写出方程
的解
;
(ii)若方程
至少有三组不同的解,写出
的所有可能取值.
(Ⅱ)证明:对任意一个
,存在正整数
使得方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46f8ac04c5eb2e4e7e8a913a847871f.png)
至少有三组不同的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc1f6effac6aa2324b0ef6c99174557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17827b180be7fe6257a170ac4f14ba0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e247a6c2ea97079d54f63f8c4c56f10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c537b60bc58957d4b11a33bc8a4bd.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e935b5d0182c2382de28c46cb968af3.png)
(i)写出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71896c05d453bb24a4e637e20ce29453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f9324832985ae572814995c623205a.png)
(ii)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f093c9f09fb55bdce94f35d51656472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(Ⅱ)证明:对任意一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924e716802ea0e503812d4168de1ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46f8ac04c5eb2e4e7e8a913a847871f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c920b1a53dc473254e2b0f5b4fd4db0a.png)
您最近一年使用:0次
2018-03-31更新
|
1346次组卷
|
6卷引用:北京市朝阳区2018年高三一模数学(理)试题
名校
3 . 已知集合
,
,设集合
同时满足下列三个条件:①
;②若
,则
;③若
,则
.
(
)当
时,一个满足条件的集合
是__________ .(写出一个即可).
(
)当
时,满足条件的集合
的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2dd2c7f4bf194e5cf83eb8e01f491f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827e0933211772799f65eccd2fbce592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde2827722685b8a71f9aae2dc4d7484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc1108d22143e834bd69eeb9fd8775a.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2017-10-31更新
|
1180次组卷
|
5卷引用:北京市朝阳陈经纶中学2016-2017学年高一上期中数学试题