12-13高一上·北京·期末
名校
1 . 已知集合
,若集合
,且对任意的
,存在
,
,使得
(其中
),则称集合
为集合
的一个
元基底.
(1)分别判断下列集合
是否为集合
的一个二元基底,并说明理由;
①
,
;
②
,
.
(2)若集合
是集合
的一个
元基底,证明:
;
(3)若集合
为集合
的一个
元基底,求出
的最小可能值,并写出当
取最小值时
的一个基底
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806fb311a1ddd23364eb67dc6eaf9aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb33db56afdfe2e6b023d001b8c7314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a347b942334e794abc5d1a583e8b434d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64950c9fd9dc31394b2e00401d1b70ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ad20a92aea25d3d1800ec6cb93699c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)分别判断下列集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453c0f95e052beb1edece487d9cab07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522954ce536d559cf03638d87fad504c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4863b95f36a4af59514b7c77e02e30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3757ba09c1d5ceb4632a8ddd47230902.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2413015bd5826b340903708cc7750a0b.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc98f4e6c9f9a1dc1080d0e0998fc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2023-03-22更新
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1066次组卷
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15卷引用:2011-2012学年北京市育园中学高一第一学期期末考试数学
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2 . 已知集合
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
中所有不同值的个数.
(1)若集合
,求
;
(2)若集合
,求证:
的值两两不同,并求
;
(3)求
的最小值.(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ce6be5490570923b903dd8b41af21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34eab5752f27333c8764b320fe5ea92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a6fdf9a72190e86809b49ac0496f7d.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdbe456b157ab21b970a5b59308125b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a17ac17c60f8f287167afce4662b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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