23-24高三上·上海浦东新·期中
名校
1 .
是正整数集的子集,满足:
,并有如下性质:若
、
,则
,其中
表示不超过实数
的最大整数,则
的非空子集个数为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793b9b22f06177785864b283ff38d61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b958eb9d7d286a1c6daf4711f304b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
2 . 对非空整数集合M及
,定义
,对于非空整数集合A,B,定义
.
(1)设
,请直接写出集合
;
(2)设
,
,求出非空整数集合B的元素个数的最小值;
(3)对三个非空整数集合A,B,C,若
且
,求
所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff97e9f30e667709fc602b8dcc7523e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ef9a7e4979cb5c0e8f4ff92af351dc.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679a7e0835c8200dc4975baf3e89d058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b9f7e0aa69227773cb9d9b7bb6244.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2463f83ca63b14937787c99fcd1958d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e79b6edfd5f5bb3866599fcb2aa6f3.png)
(3)对三个非空整数集合A,B,C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fcff4bcf7a1e6652774a5aee4519c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72944e6acd452acaa213f6ae23ae9a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6e825795c828f8281e93607d0e1b1.png)
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2023-11-05更新
|
1340次组卷
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4卷引用:2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19
(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)专题1 集合新定义题(九省联考第19题模式)讲江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题北京市清华大学附属中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
3 . 已知
元正整数集合
满足:
,且对任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
,写出所有满足条件的集合
;
(2)若
恰有
个正约数,求证:
;
(3)求证:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5fcfc55b56f04ac530871067e5ce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5ba5a3d48da1d7f3952c013a5ee0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ae1c18e2cded6d04808a3aa24c6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c7cb34e9b5c1ecd75ff1966e882ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e81d3dacb5e2e527b8daebcf19fc9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7979eac1b85b681ba94bf8d833c5c6e7.png)
(3)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa673986cef1873a421a572abf9ed71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cee7a77f2f4592cb5c96245ff025f8.png)
您最近一年使用:0次
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4 . 记
,
,存在正整数n,且
.若集合
满足
,则称集合A为“谐调集”.
(1)分别判断集合
、集合
是否为“谐调集”;
(2)已知实数x、y,若集合
为“谐调集”,是否存在实数z满足
,并且使得
为“谐调集”?若存在,求出所有满足条件的实数z,若不存在,请说明理由;
(3)若有限集M为“谐调集”,且集合M中的所有元素均为正整数,试求出所有的集合M.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b375ce40fbaba527a0ca9a536dcb2839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072a103be06a46fb5a8804ca7c4d97ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4662f1ff44acc2a6aa89f37698fe2a6.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e5c92600dc103d576d31a09847450a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d032fcb21b8d4ecdbfdec9c4fafed7cb.png)
(2)已知实数x、y,若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1eefbb4adb98f74d1508bb663166ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/409ced5ce5ace28fd617f7c4be418ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51da43ae375c45bb65f0cacf008919e2.png)
(3)若有限集M为“谐调集”,且集合M中的所有元素均为正整数,试求出所有的集合M.
您最近一年使用:0次
2023-10-13更新
|
396次组卷
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4卷引用:数学(北京卷03)
名校
解题方法
5 . 设集合
,其中
.若集合
满足对于任意的两个非空集合
,都有集合
的所有元素之和与集合
的元素之和不相等,则称集合
具有性质
.
(1)判断集合
是否具有性质
,并说明理由;
(2)若集合
具有性质
,求证:
;
(3)若集合
具有性质
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d7759d382dfd33b5a08fa4592b5178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d267c89385033926ef80e9b65f45a15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1100967c4704ee3f4eddc759f565a75.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baccb9bfcf79366c4605055b9ce5c2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8e17568e91b25776648c078886ee07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f95d6428ee9a829917262324c03ab4.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dfa7b5f718ed24cde77b169b3d76f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706182007fed7b3cf14e78cbb47fda42.png)
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解题方法
6 . 从集合
的非空子集中随机取出两个不同的集合
,则在
的条件下,
恰有1个元素的概率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cea90e212e75cde4ac6baf48eac94ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7dcbd7f44645b8c707627ab0795e18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
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2023-10-01更新
|
444次组卷
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2卷引用:浙江省金华十校2023-2024学年高三上学期11月模拟考试预演数学试题
名校
7 . 设m是实数,已知集合
,集合
,且
,则m的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc088345fb1d4cfdda89d068dd0f93d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104668ced17a26db2ae1862b9f0b23c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63128a77392afc5f8b873b7a67f2b5f.png)
您最近一年使用:0次
2023-09-11更新
|
767次组卷
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4卷引用:上海市敬业中学2024届高三上学期开学考试数学试题
上海市敬业中学2024届高三上学期开学考试数学试题海南省海口市琼山华侨中学2023-2024学年高二上学期期中考试数学试题海南省省直辖县级行政单位澄迈县澄迈中学2023-2024学年高二上学期期中数学试题(已下线)2.1.4 圆与圆的位置关系(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
23-24高三上·北京·开学考试
名校
8 . 正实数构成的集合
,定义
.当集合
中恰有
个元素时,称集合A具有性质
.
(1)判断集合
,
是否具有性质
;
(2)若集合A具有性质
,且A中所有元素能构成等比数列,
中所有元素也能构成等比数列,求集合A中的元素个数的最大值:
(3)若集合A具有性质
,且
中的所有元素能构成等比数列.问:集合A中的元素个数是否存在最大值?若存在,求出该最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cb23bb13473e9f87969f2ef5e7782a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e379930acfab9812a8747177c82bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0ebbec9ed95737da28127df0006e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09b60535bb9fec40ebca4fb3f53adb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efabd340d3aa9821a8b08436f9d258c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94672690f659abc9c06b44be519bc51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)若集合A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0ebbec9ed95737da28127df0006e9c.png)
(3)若集合A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0ebbec9ed95737da28127df0006e9c.png)
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9 . 对于数集
(
为给定的正整数),其中
,如果对任意
,都存在
,使得
,则称
具有性质
.
(1)若
,且集合
具有性质
,求
的值;
(2)若
具有性质
,求证:
;且若
成立,则
;
(3)若
具有性质
,且
为常数,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4622c700325a90d453e6300b886a8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bc1a0bba5e6e8ddf6f1f60f78e6490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dbbefb5a9955cdbe090c5f0b8a8d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cbab5722e0fb2df79a07cfe8f1164b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7511e6ce72a5232820b7007f976be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864dd49f786346bc320deace92f949b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551ee6e86b2c6e79236dfe3e2e2c24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346549f9adda7eb363f16d355ae68b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cf27bef9cafda3dd897e29f3fe1df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
您最近一年使用:0次
10 . 对任意正整数n,记集合
,
.
,
,若对任意
都有
,则记
.
(1)写出集合
和
;
(2)证明:对任意
,存在
,使得
;
(3)设集合
.求证:
中的元素个数是完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39352d44787ecda055946f530893f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5359f5f086b89cc656cdd4f79a3b7baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df0913f90131b298c8f6f57437f69b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c1352dca7dc3caf67c1cb937d52795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35755ad07f05e7bfe00176d6334389f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a28908216e6879a09b372d957be1e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e840ba7606959ccea36793f3ef0775d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b576952835af1f3492f0f3e6d00093e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112d102cbe7ce2bebe0c76e87e89a00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-11-15更新
|
161次组卷
|
4卷引用:北京市朝阳区2022届高三上学期期末统一检测数学试题