题目
题型:解答题难度:一般来源:不详
已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114215-95464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114216-75709.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114216-32713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114216-44767.gif)
A与B之间的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114216-22813.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114216-62034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-81354.gif)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-44413.gif)
(Ⅲ) 设P
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-22626.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-49802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-64516.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114217-49802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-10273.gif)
(考生务必将答案答在答题卡上,在试卷上作答无效)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-78059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-38723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-72609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-47487.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-43457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-75780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-16295.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-76720.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114220-66827.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114220-47875.gif)
由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-43457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114220-16412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114220-34849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114220-62270.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-76720.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114221-86202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114221-78369.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114221-65092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114221-61937.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114221-53508.gif)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-78059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-38723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114218-72609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114219-47487.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114222-19869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114222-57402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114222-29217.gif)
记
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114222-42582.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114222-92169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114223-42030.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114223-94617.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114223-73524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114223-76443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114223-17244.gif)
个数为
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-23326.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-40960.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-17518.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-91386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-69684.gif)
由此可知,
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114225-80127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114225-38873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114225-13141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114225-55907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114225-45168.gif)
(III)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-79861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-22734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-83043.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-83043.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114224-91386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-86274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-47583.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-22734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114227-45314.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-86274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114227-72476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114227-25952.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114226-22734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114227-10406.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114227-34413.gif)
核心考点
试题【(本小题共13分)已知集合对于,,定义A与B的差为A与B之间的距离为(Ⅰ)证明:,且;(Ⅱ)证明:三个数中至少有一个是偶数(Ⅲ) 设P,P中有m(m≥2)个元素】;主要考察你对集合运算等知识点的理解。[详细]
举一反三
设
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114212-55501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114213-22808.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114209-72665.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114207-38620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114207-82502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114208-69313.gif)
A.(0,2) | B.[0,2] | C.{0,2] | D.{0,1,2} |
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114204-37336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114204-50089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114205-28040.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114202-52857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190817/20190817114202-84382.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
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