题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005427-34609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005427-71984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-13966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-58255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-68919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-64862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-23504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-89350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-56440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-13966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
(I)检验集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-34417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-25603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
(II)对任何具有性质
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-13966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-35725.png)
(III)判断
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-23504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-39677.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-23148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-12204.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-35725.png)
(III)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-54813.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-34417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-25603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-88850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-23148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-12204.png)
(II)证明:首先,由
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-13966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-49794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-83204.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-84337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-26766.png)
又因为当
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-89350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-56440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-56440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-60785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-66377.png)
从而,集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-77428.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005430-35725.png)
(III)解:
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-54813.png)
(1)对于
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-48285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-89350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-63132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005433-82602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005433-94681.png)
如果
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-64862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005433-60806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-17212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-66665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-64772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-66665.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-65467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-35585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
可见,
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005435-29634.png)
(2)对于
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005435-67477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-89350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005432-63132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005435-51575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005435-43138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-64862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005433-60806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-17212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-66665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005435-97154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005434-66665.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005436-40925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005436-89579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
可见,
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005429-25989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005428-12009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005436-86005.png)
由(1)(2)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005431-54813.png)
核心考点
试题【已知集合,其中,由中的元素构成两个相应的集合:,.其中是有序数对,集合和中的元素个数分别为和.若对于任意的,总有,则称集合具有性质.(I)检验集合与是否具有性质】;主要考察你对集合的概念与表示等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005422-17024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005422-86073.gif)
(1)自反性:对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005422-20897.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-63451.gif)
(2)对称性:对于
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-60560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-95181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-47214.gif)
(3)传递性:对于
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-33829.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-95181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005423-25819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005424-52022.gif)
则称“
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005422-86073.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005422-17024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005420-49041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005420-79616.gif)
A.{1,2} | B.{0,1,2} | C.{x|0≤x<3} | D.{x|0≤x≤3} |
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005419-41912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005419-47453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005419-72688.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005419-39592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005419-98929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005417-93048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005417-15349.gif)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005417-41920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005417-70439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005418-46524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005418-13821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005409-76918.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005409-99269.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815005409-38121.gif)
A.a<1 | B.0<a<1 | C.a="1" | D.a>1 |
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