1 . 集合
由有限个实数组成,定义集合
的离距
如下:实数轴上,集合
中的每个实数
对应一个点
,实数
对应的点
与所有这些点
的距离的算术平均数记为
,称函数
的最小值为集合
的离距,记为
.例如,集合
的离距是0,集合
的离距是2.
(1)分别求出集合
的离距;
(2)求数集
的离距;
(3)已知非空数集
满足
,试写出一个关于
的大小关系的等式或不等式,并给出证明.
![](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/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e51c8010a4568d7d44f261973dea420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39412925212a989c503e891db840609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
(1)分别求出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384a3e8b9a7ffb00bb124ba97b7c992.png)
(2)求数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22accc2928d3370f48a84cc4703a4b07.png)
(3)已知非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e6c4bb62b14f8e70d8f8b1ac911bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3598ab9c4ac9a9496c5f34b9b5fda3cf.png)
您最近一年使用:0次
名校
2 . 设数阵
,其中
.设
,其中
且
.定义变换
为“对于数阵的每一行,若其中有
或
,则将这一行中每个数都乘以
;若其中没有
且没有
,则这一行中所有数均保持不变”
表示“将
经过
变换得到
,再将
经过
变换得到
以此类推,最后将
经过
变换得到
.记数阵
中四个数的和为
.
(1)若
,写出
经过
变换后得到的数阵
,并求
的值;
(2)若
,求
的所有可能取值的和;
(3)对任意确定的一个数阵
,证明:
的所有可能取值的和不超过
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc547069ea30c6fd86a2002412dcbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ad77a51a408977ca4eadd84cf7af68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c58425afdfb13f4c9671ad938046e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b41f4fbe3615ad2e6055e83792015c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c866e176c39fd314d3cd3bbe52ba8ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13457c887234afca68b4ab6be353481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfe5a8c2dd8ab99cc48f249329606e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4891337ce2ce5c1f700b8824a03cd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747f43f06177d471d83cda317c39d105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d04c7fa3af0dfe844bad6469e0e91fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221f88f10c065cf9c855369540113c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15145fa7ce87d4730373560c26d292bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dbb44d7459e2c69c046775664c21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dbb44d7459e2c69c046775664c21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18267d0ffae48f0e6cdd7db1e2ab8f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ba94d55e995adb5a98232d720637e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4f007b1ceaccfff1d659f6f8592c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18267d0ffae48f0e6cdd7db1e2ab8f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6131d017f185f950dfbbdc9e3c7080e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18267d0ffae48f0e6cdd7db1e2ab8f2.png)
(3)对任意确定的一个数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18267d0ffae48f0e6cdd7db1e2ab8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
您最近一年使用:0次
2023-12-20更新
|
1843次组卷
|
6卷引用:北京市海淀区中关村中学2024届高三上学期12月月考数学试题
北京市海淀区中关村中学2024届高三上学期12月月考数学试题浙江省温州市第五十一中学2024届高三上学期期末数学试题(已下线)最新模拟重组精华卷2 -模块一 各地期末考试精选汇编(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)
名校
3 . 已知
为所有
元有序数组
所组成的集合.其中
(
).
对于
中的任意元素
,
定义
,
的距离:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1138a3e79624a1fe9bc03b5300d9483.png)
若
,
为
的子集,且有
个元素,并且满足任意
,都存在唯一的
,使得
,则称
为“好
集”.
(1)若
,
,
,
,
,
,求
,
及
的值;
(2)当
时,求证:存在“好
集”,且“好
集”中不同元素的距离为5;
(3)求证:当
时,“好
集”不存在.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de4e0337716e1d89eb1a6cfd7b8335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a406d53fd6ffd9ee6cd914f5e2b0a9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94a179746b8c763e5620ac724ff1147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f2d8a263129fd9df23224bcd54d25e.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/a1138a3e79624a1fe9bc03b5300d9483.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6bc55d5eb2c3d085b62ffcd8d138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0dce56f4a3a33c63f59cb4e79fdd4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98aa5f1acb67ec4580d240c2525e4d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ff114e0ec7de68f1239f70f68152b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd7ef0582648cdadc44efeff970f349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b733d1c7e28ba1380d76ef991a0e896e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b339e4303d066bc297c22b72ecb324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f945af9e01c29c5b3a8da1d640e910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3bf525a4089739d372536e76d625d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e753949e45a5c315b622a27cb22138dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ea1cb8084df487fa8b6d1956c6e8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f10adb388c64ee1f164269219d9afc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c93bd6883272a1c27f8a04f5901fc63.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc329b32ecf0f0532d09a8a21343e8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
4 . 若函数
的定义域为D,集合
,若存在非零实数t使得任意
都有
,且
,则称
为M上的
增长函数.
(1)已知函数
,函数
,直接判断
和
是否为区间
上的
增长函数;
(2)已知函数
,且
是区间
上的
增长函数,求正整数n的最小值;
(3)如果
是定义域为
的奇函数,当
时,
,且
为
上的
增长函数,
求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe5fa85f3ebdfca5b2c131582e54bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137e19310362e379bd5943525b715aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44732202502102fe40f23c7558d1ab5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d2f074101ec58868493992814a2ff9.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7c91c7cad8a060981951c082cb9291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f6a0eff55217e08cd9c7268ef3eecb.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facd6be947e37552dfa0565d1f21e380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d94112851ce0deb4761bf00fcf275ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8559db5cec89fb0ed29e8be8fdb0b1.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012e8b22975a0984bce88e0a8148a61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
求实数a的取值范围.
您最近一年使用:0次
5 . 已知点集
.设非空点集
,若对
中任意一点
,在
中存在一点
(
与
不重合),使得线段
上除了点
外没有
中的点,则
中的元素个数最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b22251511d66ad0c49513dae61f2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fcd91711251a8bfe28b22c870dad80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fb56e714978b3dd418996c1f75768c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
解题方法
6 . 对于非空有限整数集X,
,定义
,对
现有两个非空有限整数集A,B,已知
且
.
(1)当
时求集合B;
(2)证明:
;
(3)当
且
时,任取
构造函数
问:当a,b取何值时,
的最小值最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9451ce4fed053674ea20d5b455b783d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb70a272d3abd0bb156e332e75dc36b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cd3b18a04c9a72a0bf7791bdf56a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9a194c0b9152e11aabc059c8483b93.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba387b457949fde336790c9d05c4f1c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15d281a85375fcf633d2cd86e294028.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eeee50bc500aad281fbb28d465db5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4a0f5fcd7882200fa25b6ee5143f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c41c277675b413bbff28387082c9785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbad171aea431ed7347bcdc7fbef54d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
7 . 已知集合
,任取
,
,定义
,其中
表示
,
中的最大值,例如
,
.
(1)当
且
时,写出满足
的所有元素
;
(2)设
,
满足
,求
的最大值和最小值;
(3)若
的子集
满足:
,
成立,求集合
中元素个数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395a9ac66a8eac79bff4b9fabd5ba478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a7960dfe0fa502affe34fc991637e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3f8a94c75d26f9ebdce6faac093844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51767af8e9e891862fddceaddf69771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9d48e670be1ddbfee3738824a7eccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca7c352f4aaaca488dff1fb304874bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca92c9a09bd82e0ebe8e065e09bfbc9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd704df7736c0dd309029639b2894483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6be0211acf7ee73b64b29f4ee133d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9e7c92fe16d2d9140e2ce9d554d3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5d3909dcc134e61ec890a963768ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520cb52f2ae9917330a3a54a08268e62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadf7483681e66386d3a4cc2a6f818b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774d57a142a02c766cfe86bdecd98a90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffd40374a860c7e9f69972596c58ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a46b9258e95510df09da8c168ce09e.png)
您最近一年使用:0次
名校
8 . 已知自然数集
,非空集合
.若集合E满足:对任意
,存在
,使得
,称集合E为集合A的一组m元基底.
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
;
②
.
(2)若集合E是集合A的一组m元基底,证明:
;
(3)若集合E为集合
的一组m元基底,求m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaa2be7b1653f2371891e9a794f023d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5002b44e87e59f1e1fda6a841de5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c059a6234c274a3aa626b20698263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53613f4c8d697ad45bd08f29ef76f19e.png)
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93b026b2bd1f754bcee49e48c6bbb4.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3210812ece496c3ab3396e9ec2f0c6e.png)
(2)若集合E是集合A的一组m元基底,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e41403eba28ee0f497c79953b842ca1.png)
(3)若集合E为集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1341ae10a275cd370eb014d0f505f3.png)
您最近一年使用:0次
2023-11-03更新
|
377次组卷
|
2卷引用:北京市人大附中2023-2024学年高二上学期期中数学试题
名校
解题方法
9 . 对非空数集T,给出如下定义,
定义1:若
,
,当
时,
,则称T为强和差集;
定义2:若
,
,当
时,
,则称T为弱和差集.
(1)分别判断
是否为强和差集,
是否是弱和差集,并说明理由;
(2)若集合
是弱和差集,求A;
(3)若强和差集B的元素个数为12,且
,求满足条件的集合B的个数.
定义1:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d81972b1768d827ba3083f96a273412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760be062c0e1175db3cf059302e9893b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3866ffa03f828d57269c805c08e8c13a.png)
定义2:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d81972b1768d827ba3083f96a273412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b722d685d1c56d4d29ba137db59e25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf655e7150f4759685df48b605dc8f2.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b2be1b0b6bea70d4e64894f1009359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ab4879d5e412739c7aeba46dd0ffdb.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039abfbcdcc01da76d4123f81cf0f6a5.png)
(3)若强和差集B的元素个数为12,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d1c7c644d841c90d84dd75c562d9e.png)
您最近一年使用:0次
名校
10 . 设正整数
,集合
,对于集合
中的任意元素
和
,及实数
,定义:当且仅当
时
;
;
.若
的子集
满足:当且仅当
时,
,则称
为
的完美子集.
(1)当
时,已知集合
,
.分别判断这两个集合是否为
的完美子集,并说明理由;
(2)当
时,已知集合
.若
不是
的完美子集,求
的值;
(3)已知集合
,其中
.若
对任意
都成立,判断
是否一定为
的完美子集.若是,请说明理由;若不是,请给出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9f20576d4bb73cc3c0d62b574e23eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a2f4ee8d35d21bbef8edde88c6bd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759aff07fb4c591cdcb4dd7c2af6dd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279ec05658fd1933d7d0a8c56d1afca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b7ca4667865ebe617fa6539e8d11fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fec1f2fef63966d161ebaf6bd40825e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b266fc4302ece42971e9f2545ffb1b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a0812b120ad354e735cb3f11fa89f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2528fbb6a59ba983d1a70c81b0886484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce88f9aba3036bf425a682829cdd441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8406e10f6c518b911ad97501da658cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72a181077702c7f5b744ca57db0af23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5b01bbb185b5a804ce11df2a06cdab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3ea3c78cb3609e207a7ce2c3915ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c6eb534c175e2676ed45657c71df01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92247b24065617e962c85a52086261f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2023-10-10更新
|
287次组卷
|
2卷引用:北京市东直门中学2024届高三上学期阶段检测(10月月考)数学试题