1 . 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)
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2023-11-15更新
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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
名校
2 . 已知
是各项均为正整数的无穷递增数列,对于
,定义集合
,设
为集合
中的元素个数,若
时,规定
.
(1)若
,写出
及
的值;
(2)若数列
是等差数列,求数列
的通项公式;
(3)设集合
,求证:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b4acf7b25b750fbe7205fd179b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857369257ea1b23ef40ce7e3a0f058af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1202d58cd3ad66e7b23f01024566705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc57d8a4f67a040435d8b206d3254bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6510d0816033afa001c130342bb7cda.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54e4701d4cb8d0133ad2044a7e0f52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1479e28bf6a8cb64ec7df77cd295f99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
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2024-01-21更新
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7卷引用:北京市朝阳区2024届高三上学期期末数学试题
北京市朝阳区2024届高三上学期期末数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)讲(已下线)2024年高考数学二轮复习测试卷(北京专用)(已下线)黄金卷01(2024新题型)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷
3 . 若集合
(
)满足:对任意
(
),均存在
(
),使得
,则称
具有性质
.
(1)判断集合
,
是否具有性质
;(只需写出结论)
(2)已知集合
(
)具有性质
.
(
)求
;
(
)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308975da991b918217d1ee03ad1830ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09737e117adb481fd3c4affdf38ff45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0a9f2d0e6e1c56d862a178f1d4a1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7bf76d1e4ec87759a61a5fda954515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735cf07db1fd80a115aa5fb5213289ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee42f4c9aa90c833e0c9e3d997c7c732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308975da991b918217d1ee03ad1830ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ab6567c156fee308640828a804415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3d8d73a7dea024f7e07a3b6985dcb2.png)
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2022-01-24更新
|
546次组卷
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5卷引用:北京市门头沟区2022届高三上学期期末调研数学试题
北京市门头沟区2022届高三上学期期末调研数学试题北京市第十四中学2022-2023学年高二下学期期中测试数学试题(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)专题01 集合与常用逻辑用语3-寒假作业单元合订本北京市广渠门中学2022-2023学年高二上学期9月月考数学试卷
4 . 设
为给定的不小于
的正整数,考查
个不同的正整数
,
,
,
构成的集合
,若集合
的任何两个不同的非空子集所含元素的总和均不相等,则称集合
为“差异集合”.
(1)分别判断集合
,集合
是否是“差异集合”;(只需写出结论)
(2)设集合
是“差异集合”,记
,求证:数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1557d3b215f58330d34827b134ad2925.png)
;
(3)设集合
是“差异集合”,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1c0645b3b48cbc3840164af821916b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d8838c9136ed8ba75eb0293c74b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8887c3ec8c7554225df9938ed0fd9f7b.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1c0645b3b48cbc3840164af821916b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d84828745b5efff020a705a15a019b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773f8c0f02c7c2e2cfe8d26265179fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1557d3b215f58330d34827b134ad2925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f736b66000c6c6befe2171d5090bf1.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1c0645b3b48cbc3840164af821916b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749877d42d1984fb42369b7bb4e376c7.png)
您最近一年使用:0次
2020-01-11更新
|
498次组卷
|
2卷引用:北京市房山区2019-2020学年高三上学期期末数学试题
名校
5 . 设有二元关系
,已知曲线
.
(1)若
时,正方形
的四个顶点均在曲线
上,求正方形
的面积;
(2)设曲线
与
轴的交点是
,抛物线
与
轴的交点是
,直线
与曲线
交于
,直线
与曲线
交于
,求证直线
过定点,并求该定点的坐标;
(3)设曲线
与
轴的交点是
,
,可知动点
在某确定的曲线
上运动,曲线
上与上述曲线
在
时共有4个交点,其坐标分别是
、
、
、
,集合
的所有非空子集设为
,将
中的所有元素相加(若
只有一个元素,则和是其自身)得到255个数
,求所有正整数
的值,使得
是一个与变数
及变数
均无关的常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489a58805c72dcadc4abd8c4588165d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912af898055c5dabdf767a3cf7b2d8f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8636fedba520535bd22f80a257cce15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4a63d14654c66cc71bf26293d698ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(3)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa5463bb430fa36159237b0238363c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfbe53ce5fd04beb18203214b662573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fd0f89e7a74e6a1269ea3f60383f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7351e10351e2216540c194735cb24039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0db9725b166638962758593bff482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d10abb19c5f496ed322c2f4bcd5cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a25362614aa93807f5bc0adec1f585b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e27aa0c05e4f20fd9b06ec3aec7c9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac2a1b17f01e120dc4d1b35db181269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc00379c7af113543302417b685c7d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc00379c7af113543302417b685c7d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad9f4dff95110a7ca7386523010b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92784299c483916224b45d36c5e82363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b49387212190fca877a8f280aa4c37.png)
您最近一年使用:0次
2020-01-02更新
|
490次组卷
|
3卷引用:上海市南洋模范中学2017-2018学年高三上学期期末数学试题
6 . 设数组
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
,数
称为数组
的元素.对于数组
,规定:
①数组
中所有元素的和为
;
②变换
,
将数组
变换成数组
,其中
表示不超过
的最大整数;
③若数组
,则当且仅当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
时,
.
如果对数组
中任意
个元素,存在一种分法,可将其分为两组,每组
个元素,使得两组所有元素的和相等,则称数组
具有性质
.
(Ⅰ)已知数组
,
,计算
,
,并写出数组
是否具有性质
;
(Ⅱ)已知数组
具有性质
,证明:
也具有性质
;
(Ⅲ)证明:数组
具有性质
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad5b09d32784527e9d1201abb4ef099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9fcb34bf3a74eae571ddad293b6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb10fbfb7eb6d4d4ffd799cc5a363b4.png)
②变换
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916765ac224780b2ab9ad42c16b279c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
③若数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd9a9a948c76032a62a91d11fbf5bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9fcb34bf3a74eae571ddad293b6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7cbcf6e8ea569285cd05a6126d7190.png)
如果对数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅰ)已知数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5994d78fc5debd0469e2a212561751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1a7b15221d91714fcb964379e1e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292a7444b7e76515cee05ffe1eea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de0f6d2b676fb885e43df4db0ed66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅱ)已知数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b373da1d03d8fe9f96f75a1d310a24d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅲ)证明:数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50513a655f357615a650b63daf00be2c.png)
您最近一年使用:0次
名校
解题方法
7 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2019-02-01更新
|
577次组卷
|
6卷引用:上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题
上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题上海市七宝中学2020届高三上学期11月月考数学试题上海市曹杨二中2019-2020学年高二上学期期末数学试题北京市东城区景山学校2021届高三上学期期中数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21北京市密云区第二中学2024届高三上学期10月月考数学试题
8 . 已知集合
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
中所有不同值的个数.
(1)若集合
,求
;
(2)若集合
,求证:
的值两两不同,并求
;
(3)求
的最小值.(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ce6be5490570923b903dd8b41af21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d2b07ef113af3d7de279f09c03956b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34eab5752f27333c8764b320fe5ea92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a6fdf9a72190e86809b49ac0496f7d.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdbe456b157ab21b970a5b59308125b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a17ac17c60f8f287167afce4662b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcbe244cf309094c2815fc3d6407125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
9 . 对于任意的n∈N*,记集合En={1,2,3,…,n},Pn=
.若集合A满足下列条件:①A⊆Pn;②∀x1,x2∈A,且x1≠x2,不存在k∈N*,使x1+x2=k2,则称A具有性质Ω.如当n=2时,E2={1,2},P2=
.∀x1,x2∈P2,且x1≠x2,不存在k∈N*,使x1+x2=k2,所以P2具有性质Ω.
(1)写出集合P3,P5中的元素个数,并判断P3是否具有性质Ω.
(2)证明:不存在A,B具有性质Ω,且A∩B=∅,使E15=A∪B.
(3)若存在A,B具有性质Ω,且A∩B=∅,使Pn=A∪B,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9df41d67a96fb8ffc19bbbcf5597dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2623bcade9e7521db92dfcb45b90f91.png)
(1)写出集合P3,P5中的元素个数,并判断P3是否具有性质Ω.
(2)证明:不存在A,B具有性质Ω,且A∩B=∅,使E15=A∪B.
(3)若存在A,B具有性质Ω,且A∩B=∅,使Pn=A∪B,求n的最大值.
您最近一年使用:0次