【题文】已知集合,求(1)当时,中至多只有一个元素,求的取值范围; (2)当时,中至少有一个元素,求的取值范围;(3)当、满足什么条件时,集合为非空集合。
题型:难度:来源:
【题文】已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133754-67931.png)
,求
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133754-88352.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
中至多只有一个元素,求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-78678.png)
的取值范围;
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26515.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
中至少有一个元素,求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-78678.png)
的取值范围;
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-78678.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-10353.png)
满足什么条件时,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
为非空集合。
答案
【答案】(1)(2)(3)见解析.
解析
【解析】
试题分析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
中至多只有一个元素包括只有1个或没得元素,只有一个元素分两种情况,故需分类讨论;(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
中至少有一个元素,包括恰有1个元素和由2个元素,注意字母a的讨论;(3)集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133755-26092.png)
为非空集合包括有一个元素,有2个元素,有一个元素需分a是否为0来讨论,有2个时只需
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-28821.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-34505.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-32772.png)
其中:当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-32772.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-61668.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-89727.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-97856.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-37306.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-65283.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133758-53089.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-32772.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133758-53089.png)
其中:当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-32772.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-61668.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-89727.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133757-97856.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133758-39438.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-28821.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133756-32772.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133758-42058.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133758-50045.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133759-27119.png)
考点:集合与元素
举一反三
【题文】集合A={x|x
2-ax+a
2-19=0},B={x|x
2-5x+6=0},
C={x|x
2+2x-8=0}.
(Ⅰ)若A=
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133734-15815.png)
,求a的值;
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133734-87189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133734-66227.png)
A∩B,A∩C=
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133734-87189.png)
,求a的值.
【题文】设全集U是实数集
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133727-83195.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133727-87447.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133727-72922.png)
都是U的子集,则图中阴影部分所表示的集合是( )
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133728-64727.jpg)
【题文】(本小题满分10分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133655-70664.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133655-76210.png)
.
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133655-32426.png)
;
(2)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133655-34902.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133655-19904.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133656-94845.png)
的取值范围.
【题文】设集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133645-81178.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133645-52712.png)
=( )
【题文】(本小题满分12分) 已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133637-46403.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133638-54749.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133638-29387.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133638-91181.png)
的取值范围.
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