名校
1 . 对正整数
,记
,
.
(1)用列举法表示集合
;
(2)求集合
中元素的个数;
(3)若集合A中任意两个元素之和都不是整数的平方,则称A为“稀疏集”.已知集合
能分成两个不相交的稀疏集的并集,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a1b26aa2a8eae39c45ab0b5e4b0888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d7155d7bd00e29d2e9324a8845735b.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb82d62ae6889a177c70d3adf8a91056.png)
(3)若集合A中任意两个元素之和都不是整数的平方,则称A为“稀疏集”.已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
2 . 对非空数集
,
,定义
与
的和集
.对任意有限集
,记
为集合
中元素的个数.
(1)若集合
,
,写出集合
与
;
(2)若集合
满足
,
,且
,求证:数列
,
,
,
是等差数列;
(3)设集合
满足
,
,且
,集合
(
,
),求证:存在集合
满足
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2879c154a00d481e9b73a3fd1c56f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c14c3a132f7fed19e8298890692bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3f7bcd226dc1daa07500ffa9b57965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbaf050f74e3b87e6d2f9647fc43fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9f6ea6346066054b5c722763d6b026.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c51a72af8fefb52643a2ccfe2c0100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5867fde790c54e6a931c5d1d22b049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81439ea75624aba008bd0f6a35dbf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c51a72af8fefb52643a2ccfe2c0100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5867fde790c54e6a931c5d1d22b049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1863bbba4b8653b4c99ff67fc3edb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef61be75060a7d37c8bc03782be6530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0588c80fa0ee2598f12eb7725c2e406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c822b25dca0587cea9e29c48849de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6ce6a51538d70382465e76b6d16f52.png)
您最近一年使用:0次
2022-03-30更新
|
1764次组卷
|
4卷引用:专题01 集合与常用逻辑用语(讲义)-2023年高考数学一轮复习精讲精练宝典(新高考专用)
名校
3 . 对正整数
,记
,
.
(1)用列举法表示集合
;
(2)求集合
中元素的个数;
(3)若
的子集
中任意两个元素之和不是整数的平方,则称
为“稀疏集”.证明:存在
使得
能分成两个不相交的稀疏集的并集,且
的最大值为14.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477ac10cc039be2d2a06fad831fa523f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d7155d7bd00e29d2e9324a8845735b.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb82d62ae6889a177c70d3adf8a91056.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-10-17更新
|
958次组卷
|
6卷引用:湖南省岳阳市2022-2023学年高一下学期期中数学试题
湖南省岳阳市2022-2023学年高一下学期期中数学试题(已下线)难关必刷01集合的综合问题(3种题型30题专项训练)-【满分全攻略】(沪教版2020必修第一册)上海市大同中学2021-2022学年高一上学期10月月考数学试题(已下线)1.1 集合的运算(第4课时)上海市青浦高级中学2022-2023学年高一上学期期中数学试题(已下线)第1章 集合与逻辑(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(沪教版2020必修第一册)
4 . 设n∈N*且n≥2,集合
(1)写出集合
中的所有元素;
(2)设(
,···,
),(
,···,
)∈
,证明“
=
”的充要条件是
=
(i=1,2,3,···,n);
(3)设集合
={
︳(
,···,
)∈
},求
中所有正数之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748cbeae327ab853b3d648b1e539925c.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9039d926c1f24d3a00596a405570ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0704b318a88a83adbe29f33e3e160d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216325d35da32daa063e3e0021a44e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fe26774c21aa0cf4b6cdf518ba1cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb237a6331d0f965c0d25e18e5bf6858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be07753eab86fa9c439a65db51c9a9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2020-02-15更新
|
966次组卷
|
3卷引用:北京名校2023届高三二轮复习 专题三 集合与数列 第2讲 数列的综合应用