1 . 当
时,定义运算
:当
时,
;当
时,
;当
或
时,
;当
时,
;当
时,
.
(1)计算
;
(2)证明,“
或
”是“
”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b8043346a0a80781b0d9a7c9cecd4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f616b1f56991ee75caae3ac35208b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a05cb3647f1ad81e328f8379b51291b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6910a71dc1e164c35b110ad0d68e3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9e3cf30d7a15408ddd0697a1fcf3d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4aa46e2bdec36770ee57fe67639ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4581917005539a0806619080496676e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85349216e2fbdaa860e9f81b3924af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987270ce2ca977277b0a3d13cb20a9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb01e9ee38d5b6ab84c19789cb5af195.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a26d77e8c7e6ffc9ea9b9ed6d813a1.png)
(2)证明,“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d05a5b738133c7204d1c8f90e30ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfc50db0551c95ea1c63550750db33b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ffb9194dead5975e453628f5bac1e7.png)
您最近一年使用:0次
2 . 已知数集
.如果对任意的
,
与
两数中至少有一个属于A,则称数集A具有性质P.
(1)分别判断数集
,
是否具有性质
,并说明理由;
(2)设数集
具有性质P.若
,证明:对任意
都有
是
的因数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349165211292b1210bf4bb41c4635b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c9db263810d4412795e3c3f8e78cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf9fc9e8c9940547678ff7934363f52.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7597d02a12754d06259eaca5ab833107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05cf27f43dcf989834056b468bda50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349165211292b1210bf4bb41c4635b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2bd99a74d8bdd2fd3931a8b8cc3172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16d8a10725d196ddf59855110cebd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
名校
3 . 定义一个n元数组
,其中
或1,i、
﹐设
,
表示A和B中相应的元素不同的个数(例如,
,则
).
(1)若
,写出所有满足
的5元数组B;
(2)设
,记
的5元数组B的个数为
,求
的值;
(3)令
(n个0),
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386216116ecf49be4a0ebdddacec60bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70ee9f169cd7e6d36ddc301f2653498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f436426be5f021a8eebccc2298b6dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1411bda8a6dee80bb6387471cfe945bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092c1c15b9dfe25f62c33a23c63b9df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ece890a7ada4782024dea0f592c14a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aa6b0d8f54fa4ba22615db58834fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b44b19e29782883ea7a17ed0684154.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88e3c1464bf1ec790168779faced2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ce4001c7467ac929dd94288f6bce09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e6bd700ba1c9217f2c2598b459d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c94707f5af06686f6265f2fdaa69b85.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e725c235172819de9751e908e63ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74fb4d2ac68691e607eb7c5cdf418ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc8f86e2046efa8b4f1dd5104b11c8.png)
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4 . 若集合
具有以下性质:①
,
;②若
,
,则
,且
时,
.则称集合A是“好集”.
(1)分别判断集合
,有理数集
是不是“好集”,并说明理由;
(2)设集合
是“好集”,求证:若
,
,则
;
(3)对任意的一个“好集”
,分别判断下面命题的真假,并说明理由.
命题
:若
,
,则必有
;
命题
:若
,
,且
,则必有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2faf3937abcb6a59071c17bc6bb10f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46de01c5104b9112a688df37eadb000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd77104cc745d1e0e262122da34482d.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05551b1d4b65f27a932c33ddb1cb6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设集合
![](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/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
(3)对任意的一个“好集”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7d8e85b211a6d2aefa223c05c064ca.png)
您最近一年使用:0次
名校
解题方法
5 . 设A是非空实数集,且
.若对于任意的
,都有
,则称集合A具有性质
;若对于任意的
,都有
,则称集合A具有性质
.
(1)写出一个恰含有两个元素且具有性质
的集合A;
(2)若非空实数集A具有性质
,求证:集合A具有性质
;
(3)设全集
,是否存在具有性质
的非空实数集A,使得集合
具有性质
?若存在,写出这样的一个集合A;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72552b86b4558a36aac78c7148d6a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4970b63e04ae03e833bdb95bd52e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出一个恰含有两个元素且具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)若非空实数集A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(3)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8afa6857b5eaf945d14a6e4d7e5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
您最近一年使用:0次
2022-11-17更新
|
645次组卷
|
7卷引用:北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题
北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题(已下线)专题1.8 集合与常用逻辑用语全章综合测试卷(提高篇)-举一反三系列(已下线)重难点01集合与常用逻辑用语(9种解题模型与方法)(1)(已下线)专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)北京市东城区2021-2022学年高二下学期期末统一检测数学试题上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)专题01集合与逻辑(15个考点)(1)
6 . 若正整数集合
(
,n为正整数,且
)满足:对任意的
(
,
均为正整数),两数
与
中至少有一个属于
,则称
具有性质
.(其中
,
,…,
表示
个变量)
(1)分别判断集合
与
是否具有性质
;
(2)设正整数集合
(
,
为正整数,且
)具有性质
,证明:对任意
(i为正整数),
都是
的因数;
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b4a47672279cfe36886093807cbce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14ee48d183ca7898ad51387e41695bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14ee48d183ca7898ad51387e41695bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52783e7a39f438adf08ef7d05d8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de0224d48e1fa1ad0cba90b02b1e9bde.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dcaf423d54476e4d59e51d5e4ef7270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05cf27f43dcf989834056b468bda50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设正整数集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b4a47672279cfe36886093807cbce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06c83269110bb65bb338057722bb3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
7 . 设A是集合
的一个k元子集(即由k个元素组成的集合),且A的任何两个子集的元素之和不相等;而集合P的包含集合A的任意k+1元子集B,则存在B的两个子集,使这两个子集的元素之和相等.
(1)当n=6时,试写出一个三元子集A;
(2)当n=16时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f110c610cb7366f729f8edb50b4145.png)
(1)当n=6时,试写出一个三元子集A;
(2)当n=16时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb931a4b3eaa34e2c6f7dab5650f8af.png)
您最近一年使用:0次
8 . 设集合A为含有n个元素的有限集.若集合A的m个子集
,
,…,
满足:
①
,
,…,
均非空;
②
,
,…,
中任意两个集合交集为空集;
③
.
则称
,
,…,
为集合A的一个m阶分拆.
(1)若
,写出集合A的所有2阶分拆(其中
,
与
,
为集合A的同一个2阶分拆);
(2)若
,
,
为A的2阶分拆,集合
所有元素的平均值为P,集合
所有元素的平均值为Q,求
的最大值;
(3)设
,
,
为正整数集合
(
,
)的3阶分拆.若
,
,
满足任取集合A中的一个元素
构成
,其中
,且
与
中元素的和相等.求证:n为奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fb515ccb4e5ead5c9328e633c703cc.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0d7559d8dfa8236ca9d4b1853fbdec.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4dbc287804fded7b1d4d0b87a4adc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4892ba321f70f83dc5d3a24d904fba9f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f494d7ee74b344609e47122af349c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b145bf79ddb43eb1732e071b1effa3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
您最近一年使用:0次
名校
解题方法
9 . 设集合
,若X是
的子集,把X中所有元素的和称为X的“容量”(规定空集的容量为0),若X的容量为奇(偶)数,则称X为
的奇(偶)子集.
(1)写出
的所有子集、所有偶子集:
(2)写出
的所有奇子集;
(3)求证:
的奇子集与偶子集个数相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4f31e1a5bd72fa23aa14c84aca4620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1002e596b542ab2f5fb91f7b6d854f3.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a9905f41f59d986c227501d353641c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2022-10-09更新
|
294次组卷
|
6卷引用:1.2集合间的基本关系(分层作业)-【上好课】
(已下线)1.2集合间的基本关系(分层作业)-【上好课】(已下线)1.2 集合间的关系(精练)-《一隅三反》(已下线)高一上学期期中复习【第一章 集合与常用逻辑用语】九大题型归纳(拔尖篇)-举一反三系列(北京市第一六一中学回龙观学校2023-2024学年高一上学期10月月考数学试题(已下线)高一上学期期末复习【第一章 集合与常用逻辑用语】拔尖-举一反三系列北京市育才学校2022-2023学年高一上学期9月月考数学试题
解题方法
10 . 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
|
897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