1 . 若非空实数集X中存在最大元素M和最小元素m,则记
.下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19acf65f43bb6356c1c59d2c1a53568.png)
A.已知![]() ![]() ![]() ![]() |
B.已知![]() ![]() ![]() |
C.已知![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() |
您最近一年使用:0次
2021-04-07更新
|
1905次组卷
|
6卷引用:北京市西城区2021届高三一模数学试题
北京市西城区2021届高三一模数学试题北京五十七中2022届高三10月月考数学试题(已下线)专题01 集合与函数概念-备战2022年高考数学学霸纠错(全国通用)(已下线)专题01 集合-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)专题02 集合与常用逻辑用语常考压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)专题01 集合与常用逻辑用语4-寒假作业单元合订本
2 . 对非空数集
,
,定义
,记有限集
的元素个数为
.
(1)若
,
,求
,
,
;
(2)若
,
,
,当
最大时,求
中最大元素的最小值;
(3)若
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3537cbcff7cc15ff0cdf26de2a73b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b830a24447b3831005c9942fb263e1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed0081de4e04574dd0884c4e6077fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e18306ebf275f54eb946ddb7c38397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4be9b536fcf7bbdb422184f74db9ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e803dee8996550a8b3fb641e437709a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbae4853231076a1c59a0d37eeaf7469.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d197338ab810f6c9d31a2b67e5f352ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560882860516a9207f47ec0156975bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb1aca774c04bd0599d77a1c0c9b43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbae4853231076a1c59a0d37eeaf7469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7987e3e0432dee47d40079d5577c2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b449796bf5cff2580eb2609830f3cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbae4853231076a1c59a0d37eeaf7469.png)
您最近一年使用:0次
2020-11-02更新
|
950次组卷
|
6卷引用:北京市人大附中2021届高三年级10月数学月考试题
解题方法
3 . 对给定的正整数
,令
,
,
,
,
,
,2,3,
,
.对任意的
,
,
,
,
,
,
,
,定义
与
的距离
.设
是
的含有至少两个元素的子集,集合
,
,
中的最小值称为
的特征,记作
(A).
(Ⅰ)当
时,直接写出下述集合的特征:
,0,
,
,1,
,
,0,
,
,1,
,
,0,
,
,1,
,
,0,
,
,0,
,
,1,
,
,1,
.
(Ⅱ)当
时,设
且
(A)
,求
中元素个数的最大值;
(Ⅲ)当
时,设
且
(A)
,求证:
中的元素个数小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8608f691fb64f578cf3ee5af3cd8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e97569e91e9574c327bab94fbd9bb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659ce142c5578c660dcadacb81b8d7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93fedde9bb8f927c986094275598b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7577c2f2038fd5478e71655277a4a853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c4974696608167ebc73d9081552d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7009fe80f51263ce2d10a09bdfea9ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6440421ef1201f1e2ad00f8bfb77964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b161ad2e118a142d9aafa2e39e30b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e1862efa4931cbf76743033ad6f1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e235caa78f940a1d9c4d0e785d425d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096409e0b9a113e1e43801cf41b3d4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d0e49177363675f01a9a754a0a62cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d533b594f63c4d48135aa0a02592b89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb900b1334149968e3a28a218ecbf7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b6a2131422a8c21784d06a21b3a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606b0d7a53aa72715af4bb9508320f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced922d8d5c0697c23fa4a70cb4bf8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d533b594f63c4d48135aa0a02592b89a.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcca0e992d47f3db0be185ba861adf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811f2ad9bbe890879e63f151b37bb814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0204f76cda5ea4ced714588be1efeaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcca0e992d47f3db0be185ba861adf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811f2ad9bbe890879e63f151b37bb814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb56467959ec1abad6bf06f10125c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d415dd1391cf359512f7714d4458feee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52265b7b99204466ba6eebd6e72ba860.png)
您最近一年使用:0次
名校
4 . 有限个元素组成的集合
,
,记集合
中的元素个数为
,即
.定义
,集合
中的元素个数记为
,当
时,称集合
具有性质
.
(1)
,
,判断集合
,
是否具有性质
,并说明理由;
(2)设集合
,
且
(
),若集合
具有性质
,求
的最大值;
(3)设集合
,其中数列
为等比数列,
(
)且公比为有理数,判断集合
是否具有性质
并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db60e5bbf9b7ccd9bcfa25b13901dc9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ca8c31293db23d9e26b2630bfe38f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e4e175940ee08d81f043b7dca31027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636c838e9c10d079e5df897fce90761b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3e11cf4b0fd80e880d3dcb578396ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5541b54297a86241bb4f83f7a629d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdaed4e9e9df56d2df0f29695235f738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2db7c70d56acbfe9c2ee8520838b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e77c9cf348b80d264050fc3bf522eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1f236961600d47a45f58d6b82f60ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb2532e0b8b5cac385d6acc4836085e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cf68fbc317e5e0eae41a3837a83034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-05-13更新
|
590次组卷
|
4卷引用:2020届北京市石景山区高三4月统一测试数学试题
5 . 设
为正整数,区间
(其中
,
)同时满足下列两个条件:
①对任意
,存在
使得
;
②对任意
,存在
,使得
(其中
).
(Ⅰ)判断
能否等于
或
;(结论不需要证明).
(Ⅱ)求
的最小值;
(Ⅲ)研究
是否存在最大值,若存在,求出
的最大值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c724c6119e3e17b6181178ce7e6baf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d1fd5262cae918d9c8ef6a1bede788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f84aa794bc075d6139177cd2f59925.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbba3561714a2b7b7b675e4c319e4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b375f090c551bb2817fa942edbf9bd05.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165df5a77d87e7c534898e995f162562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbba3561714a2b7b7b675e4c319e4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5de90d938c439d3a9a8e5e1880604f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927a02889cbfc416da88181520058c3a.png)
(Ⅰ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6b5ca66b71ac5daa42ce59f19f72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432851e0d0b7a2924da29b9cc5ca1706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b3e4ab38102e50c861c13496bd215.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(Ⅲ)研究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2020-05-12更新
|
914次组卷
|
2卷引用:2020届北京市西城区高三诊断性考试(二模)数学试题
6 . 若
为集合
且
的子集,且满足两个条件:
①
;
②对任意的
,至少存在一个
,使
或
.
则称集合组
具有性质
.
如图,作
行
列数表,定义数表中的第
行第
列的数为
.
(Ⅰ)当
时,判断下列两个集合组是否具有性质
,如果是请画出所对应的表格,如果不是请说明理由;
集合组1:
;
集合组2:
.
(Ⅱ)当
时,若集合组
具有性质
,请先画出所对应的
行3列的一个数表,再依此表格分别写出集合
;
(Ⅲ)当
时,集合组
是具有性质
且所含集合个数最小的集合组,求
的值及
的最小值.(其中
表示集合
所含元素的个数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d6469b12a3e4abd19b42d9b07b14c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8e3c9f6f00803d033d60ecc03be61a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fb515ccb4e5ead5c9328e633c703cc.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e689651e8d8f5438bf5afb6e72ee1c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907c2308a58ddfd134ce4ca32b4a0cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d361f45fc89aa6f8342fe01265f2f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4232c44f99c25d566bca0a09d486cdba.png)
则称集合组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
如图,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd45164ecad44e97205eccf6473b205f.png)
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… | … | … | … |
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
集合组1:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2419512d33074cdadd38811260f693.png)
集合组2:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76cc23f1a1dc847c21068e5378d2c4b.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f176b1357961977f6305e96b1d0ca0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b13b4469180a779ebbe6fc021c1fd98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f031d1d6bbb6d25d8ad933b016b969ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9ca68ba83be22ec5cbd6eba191cbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
您最近一年使用:0次
7 . 已知集合
,其中
,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
.
若对于任意的
,总有
,则称集合
具有性质
.
(Ⅰ)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
.
(Ⅱ)对任何具有性质
的集合
,证明
.
(Ⅲ)判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8213c48030bc2cfa88da0f2a28aca2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d807832357bea22a266e63cbd7e678a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976ed3659749e70adb41abe4030b6ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604a1abd24826ba48fe69d714b1b16d0.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.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)
若对于任意的
![](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)
(Ⅰ)检验集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e565001c699e5e221ed616dd7be2bb83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0110544a65399ad66980adc3667b8b5.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)
(Ⅱ)对任何具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca7597aeef0ed7313f6f78b9658ea5e.png)
(Ⅲ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2016-11-30更新
|
3440次组卷
|
11卷引用:2007年普通高等学校招生全国统一考试理科数学卷(北京)
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