解题方法
1 . 对于数集
,
,定义向量集
,若对任意
,存在
使得
,则称X是“对称的”.
(1)判断以下三个数集
、
、
是否是“对称的”(不需要说明理由);
(2)若
,且
是“对称的”,求
的值;
(3)若“对称的”数集
,
满足:
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61b6f4ad8f11fa9c6e5268b5368df3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80db4c6ae227b62067e092f740e7a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec1c65f144bd63ed516e001e57852de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f923fcc615e579b8dda937faa9fa40c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01243e3fb9bd7a7711a593f5395b06cd.png)
(1)判断以下三个数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee021c7c1a5df78501eaca655726212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939f7dc30e48606f0aafd5ab6d9a93b5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752455799e49f846e2601304fec5d3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41130c870a38d91008b7019ae296feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若“对称的”数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61b6f4ad8f11fa9c6e5268b5368df3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4049b329e8cf711663e050e0dc9cdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007defcff0a2cfbbb6fade9a3ab53bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346549f9adda7eb363f16d355ae68b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eba583e37243f3ba166bd1c11e58498.png)
您最近一年使用:0次
名校
解题方法
2 . 已知非空集合M满足M⊆{0,1,2,…n}(n≥2,n∈N+).若存在非负整数k(k≤n),使得当a∈M时,均有2k-a∈M,则称集合M具有性质P.设具有性质P的集合M的个数为f(n),求
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f119697ef4e41edfe652afa0ac68025.png)
您最近一年使用:0次
2019-05-04更新
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1236次组卷
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3卷引用:上海市浦东复旦附中分校2023-2024学年高三下学期3月月考数学试题
上海市浦东复旦附中分校2023-2024学年高三下学期3月月考数学试题【全国百强校】江苏省无锡市第一中学2018-2019学年高二第二学期期中数学(理科)试题(已下线)专题03 集合的运算压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)