1 . 在
)个实数组成的n行n列的数表中,
表示第i行第j列的数,记
,
若
∈
,且
两两不等,则称此表为“n阶H表”,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
且
,求证:
为偶数;
(3)求证:不存在“5阶H表”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff6f8857124f7bbc5a1c65c2e83767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9ff2b00c2841318b2697b070201a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2fe368efe94c1e98309473e49a92fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d253e22a1d9709dca48c6e0c649b47bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0fdc4f349ea9634160ce08ac269691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db8c7f00e535ec1ffbb7008711b2096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8810a8ced3ca8dae09180a663275b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求证:不存在“5阶H表”.
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2023-03-14更新
|
863次组卷
|
5卷引用:北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题
北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题北京市第一0一中学2023届高三数学统练三试题北京市第十一中学2023届高三三模(5月)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)练(已下线)微考点8-1 新高考新题型19题新定义题型精选
2 . 由无理数引发的数学危机一直延续到19世纪,直到1872年,德国数学家戴德金从连续性的要求出发,用有理数的“分割”来定义无理数(史称戴德金分割),并把实数理论建立在严格的科学基础上,才结束了无理数被认为“无理”的时代,也结束了持续2000多年的数学史上的第一次大危机.所谓戴德金分割,是指将有理数集
划分为两个非空的子集M与N,且满足
,
,M中的每一个元素小于
中的每一个元素,则称
为戴德金分割.试判断下列选项中,可能成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ecb1589c3cc179e2f62507020771e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252b52fe186ca8f10398dcd32e9ce394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4815b1d16a7ae485ff0bba0b397e893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a195a4245b05754edb54660eccc9b.png)
A.![]() ![]() |
B.M没有最大元素,N有一个最小元素 |
C.M有一个最大元素,N有一个最小元素 |
D.M没有最大元素,N也没有最小元素 |
您最近一年使用:0次
名校
解题方法
3 . 设
为非空集合,定义
(其中
表示有序对),称
的任意非空子集
为
上的一个关系.例如
时,
与
都是
上的关系.设
为非空集合
上的关系.给出如下定义:①(自反性)若对任意
,有
,则称
在
上是自反的;②(对称性)若对任意
,有
,则称
在
上是对称的;③(传递性)若对任意
,有
,则称
在
上是传递的.如果
上关系
同时满足上述3条性质,则称
为
上的等价关系.任给集合
,定义
为
.
(1)若
,问:
上关系有多少个?
上等价关系有多少个?(不必说明理由)
(2)若集合
有
个元素
,
的非空子集
两两交集为空集,且
,求证:
为
上的等价关系.
(3)若集合
有
个元素
,问:对
上的任意等价关系
,是否存在
的非空子集
,其中任意两个交集为空集,且
,使得
?请判断并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5993d7b820c0b182711674de0d85a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978ef4aebb02ab0320e8ff61d7195392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba8172b545998849067b299ac4949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddf512fd22bcd30c39da2a8ef41a82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd8717bdcfbc527676ae2a80285881e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7d20713240ffa343a7b7b8da43c577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532da63ac3aa945328904b9db8b05bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928008f619c199d9375b03b63f17f0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248bff56f76fc98ac9e16b2c751bc142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/256b72e8048ad33ee1f6919b04b70ab7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若集合
![](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/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](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/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9434f864089388016b3125ac2b0e0185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac2d6c698a0ce0dce45a8682a5532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e1bef74b304061b73a02892bbf3449.png)
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