1 . 设S为满足下列两个条件的实数所构成的集合:(1)
;(2)若
,则
求解下列问题:
(1)若数列
中的项都在
中,求
中所含元素个数最少的集合
;
(2)在
中任取3个元素a,b,c,求使
的概率;
(3)
中所含元素个数一定是
个吗?若是,请给出证明;若不是,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b370157afe7d609dde703d1821b739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09256752badab8d69ae679796896ed97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6db9323925a78926837d0870f2906b.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c212ec210300a5ba11aa50d256be9f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88d1b0d1f8b7ca3c2ab6da184ba7248.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88d1b0d1f8b7ca3c2ab6da184ba7248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f802eacf0a65d88d1e8338361451c01.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d496d72389703f32ac94a7c7c60d955.png)
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2 . 用另一种方法表示下列集合:
(1)
;
(2)
;
(3)已知
,
,写出集合P;
(4)集合
,
,写出集合B.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7e3c4e0628e9191a975aec7a722618.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87841181c05aa3ada8bf6d024bf32290.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79640a479dbee5359e43753fdb286fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802788e1f219395d00a01aa03e398721.png)
(4)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e143d79c68d0314dfe387d7117353b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aeadda03cc6c74e4966d4fb4667b2ec.png)
您最近一年使用:0次
2023-05-27更新
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966次组卷
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3卷引用:1.1集合的概念与表示课后习题训练——2022-2023学年高一上学期数学北师大版(2019)必修第一册
1.1集合的概念与表示课后习题训练——2022-2023学年高一上学期数学北师大版(2019)必修第一册(已下线)第01讲 集合的概念-【暑假自学课】(人教A版2019必修第一册)1.1 集合的概念练习
名校
3 . 已知集合
满足以下条件:①
;②若
,则
.
(1)求证:集合
至少有3个元素;
(2)若集合
,写出属于集合
的两个元素,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c28ae8dcbe30dbd6872c4ede84460b2.png)
(1)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef8912d6dd9650b30db92cb056778e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-02-25更新
|
531次组卷
|
5卷引用:河南省联考2022-2023学年高一上学期期末教学诊断性考试数学试题(北师大版)
河南省联考2022-2023学年高一上学期期末教学诊断性考试数学试题(北师大版)河南省焦作市武陟中学2022-2023学年高一上学期期末数学试题(已下线)1.1 集合的概念及特征(精练)《一隅三反》系列(已下线)第一章 集合与常用逻辑用语(单元重点综合测试)-速记·巧练(人教A版2019必修第一册)广东省深圳市新安中学(集团)燕川中学2023-2024学年高一上学期10月月考数学试题
名校
4 . 设集合
,若集合S中的元素同时满足以下条件:
①
,
恰好都含有3个元素;
②
,
,
为单元素集合;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
,
是否为“优选集”;
(2)证明:若集合S为“优选集”,则
,
至多属于S中的三个集合;
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32fe32077f54b51282141c6f6217071.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296902bfc14bde752a4503d57351988a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866fcccdcf1d7bf2f73d4323b4c1c1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41e1766af890659ac91f4ed407f5a0f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7d06d943bfb67f20183899803ef150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a839a1d941f18f084505c7e8614c984b.png)
(2)证明:若集合S为“优选集”,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7060f36f24efe532ddd3f12084f36d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
您最近一年使用:0次
2023-01-19更新
|
563次组卷
|
4卷引用:北京交通大学附属中学2021-2022学年高一上学期期中数学试题
北京交通大学附属中学2021-2022学年高一上学期期中数学试题重庆市南开中学校2023-2024学年高一上学期九月测试数学试题河南省周口市周口恒大中学2023-2024学年高一上学期9月月考数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)
解题方法
5 . 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
|
880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
解题方法
6 . 已知
为有穷数列.若对任意的
,都有
(规定
),则称
具有性质
.设
.
(1)判断数列
是否具有性质
?若具有性质
,写出对应的集合
;
(2)若
具有性质
,证明:
;
(3)给定正整数
,对所有具有性质
的数列
,求
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78dab5f68d424caa15eb7686f8ac2249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae415a09c33aa3e9d1a3dab6c522dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7e9edf6d0468e0f8ca78b8bac63bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b740bc48c9718a294c11a1485fd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f21d7bf91134d8d08668cee5dacc2e8.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd984b8eee88a2c10df0e883c9ef67f.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed1adc648cc7d8fe7ac43df4b918f11.png)
(3)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-01-05更新
|
673次组卷
|
6卷引用:北京市西城区2023届高三上学期数学期末试题
名校
解题方法
7 . 对于非空数集A,若其最大元素为M,最小元素为m,则称集合A的幅值为
,若集合A中只有一个元素,则
.
(1)若
,求
;
(2)若
,
,求
的最大值,并写出取最大值时的一组
;
(3)若集合
的非空真子集
两两元素个数均不相同,且
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d2ec1a5112ce091f604a70db6ff070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91daec4d6f087fd9575aaf6556489f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bfdfd1a175a860a18587e4c21e04da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d70d5962157e2116e7f1a267153967.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb78779234085b9dbec4e3424a1a4971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819a9ba7e6e80c06082fd1af18f7f43e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e45173688d37986ac521cbe53d22ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a227a694dc404d1184578c7d278fd8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4f1149c86913354c231ad31e01fccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f61b74f81868a14729e49b982246e.png)
您最近一年使用:0次
2023-01-04更新
|
809次组卷
|
7卷引用:北京市东城区2022-2023学年高一上学期期末统一检测数学试题
北京市东城区2022-2023学年高一上学期期末统一检测数学试题河北省邯郸市魏县2022-2023学年高一上学期期末考试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列重庆市沙坪坝区部分学校2023-2024学年高一上学期9月检测(一)数学试题北京市第一零九中学2023-2024学年高一上学期12月月考数学试卷(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列北京市第二十五中学2023-2024学年高一上学期期中过程性评价数学试题
名校
解题方法
8 . 已知整数
,集合
,对于
中的任意两个元素
,
,定义A与B之间的距离为
.若
且
,则称是
是
中的一个等距序列.
(1)若
,判断
是否是
中的一个等距序列?
(2)设A,B,C是
中的等距序列,求证:
为偶数;
(3)设
是
中的等距序列,且
,
,
.求m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ceeff24d888e358d2261dc5297b4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f542b813cc3bed485d23760a4ecbec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53422543e9a9311416faf749bdda67b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca35f4615ee3791b732587e958f8033f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab4a9bfa50054c808dd8190305d0abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639ce2dc706bba6ef6b773e25fe15a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d05111e65219f66ecee0710dd5c163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1cceb7b65ea109ee8ab8af8c039271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6069b744fec0d7e00a7869ef8407c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad5b0dc4aad791035b5c4ab87bd4702.png)
(2)设A,B,C是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bbb0a939ec3c2d0414c2351f93ae5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033bbaf9efac3563ae3ac2cd3d7c6738.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e754717bc7c470f9e21fa4fe17808ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f8b0161a8f09f832d9d49a781ee51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848aeab240f0f386f3fbe1ee1d8affc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff099d9d2d0a4a0c50339ff01e16010.png)
您最近一年使用:0次
2023-01-04更新
|
1419次组卷
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6卷引用:北京市清华大学附属中学2022-2023学年高一(非马班)上学期数学期末试题
北京市清华大学附属中学2022-2023学年高一(非马班)上学期数学期末试题北京市第五中学2023-2024学年高一上学期11月月考数学试卷(已下线)专题1 集合新定义题(九省联考第19题模式)练重庆市铜梁中学校2023-2024学年高二下学期开学考试数学试题(已下线)微考点8-1 新高考新题型19题新定义题型精选重庆市缙云教育联盟2024届高三下学期第二次诊断性检测数学试题
名校
解题方法
9 . 已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554d648b90ca48861de4316d9b87a3a6.png)
(1)写出集合A的所有真子集;
(2)设全集
,求:
,
;
(3)若
,求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab82e2123711fd87885e77e5e2a36dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554d648b90ca48861de4316d9b87a3a6.png)
(1)写出集合A的所有真子集;
(2)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e55d31a45e395afe254ed791141888b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb466a3d654c9eec6bca51928cd32e31.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e07e9e144c9ca2e2e90eab6d467f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 定义两个非空数集
的“和集”为
,对有限集合
,记
.
(1)已知
,
,求出
与
;
(2)任取非空有限数集
,证明:
;
(3)
的非空子集
满足:
,都有
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c7a43079a55f6a53b1307b2b04b55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f89b4b3ad484893d998c581ad24556.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dab17f641ff493bf06551cb038cab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80d440b9478c09a6870403a8bd5cf38.png)
(2)任取非空有限数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a48c70e8d0da803583934a9fd362915.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bdeca2b562c73695cd1f5139b4d2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e532310f27fb7f3550c55c596dda168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8063f81dccffca2ca76e183bda91d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a90b4472c17fe6f9998088960a72a6.png)
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