题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-56472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-31587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-86548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-25956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-89394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
(Ⅰ)分别判断集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-35027.png)
(Ⅱ)设集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-31587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-82425.png)
(Ⅲ)对任意的一个“好集”A,分别判断下面命题的真假,并说明理由.
命题
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-33783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-31587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-66653.png)
命题
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-37879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-31587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-25956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-22551.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-58505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-49712.png)
(Ⅲ)命题
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-68575.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-99771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-95410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-14962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-32176.png)
这与
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-41896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-99771.png)
(II)根据好集的定义
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-18300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-27673.png)
(III)本小题也是先假设p、q都是真命题,然后根据好集的定义进行推证..
(Ⅰ)集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-99771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-99771.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-95410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-14962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-32176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-41896.png)
有理数集
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-58505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002711-55070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002712-41892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002712-42775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002712-93295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-25956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002712-29450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002709-58505.png)
(Ⅱ)因为集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002712-70880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-73837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-99152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-67848.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-45820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-49712.png)
(Ⅲ)命题
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002710-68575.png)
对任意一个“好集”
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002707-71983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-73837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-55624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-89436.png)
下设
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-55624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-32369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-71581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-78830.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-57397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-54007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-12614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-24051.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-81887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-25166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-72556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002716-31600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002716-83741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002715-72556.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002716-72328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002716-27010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002716-88703.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-89436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002714-89436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002717-94504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002713-73837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002717-58907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002708-89394.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002717-97003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002717-22178.png)
核心考点
试题【(本小题满分13分)若集合具有以下性质:①②若,则,且时,.则称集合是“好集”.(Ⅰ)分别判断集合,有理数集Q是否是“好集”,并说明理由;(Ⅱ)设集合是“好集”】;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/20190815/20190815002706-27121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002705-77991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002705-26025.png)
A. 3 | B.4 | C. 5 | D. 6 |
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002653-61664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002654-49308.png)
A.1 | B.2 | C.7 | D.8 |
①空集没有子集 ②任何集合都有至少两个子集
③空集是任何集合的真子集 ④若Ø
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002652-24549.png)
A.0个 | B.1个 | C.2个 | D.3个 |
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002650-44637.png)
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