📄 content-4-4-1.htm
字号:
<html>
<head>
<title>bibao</title>
<meta http-equiv="Content-Type" content="text/html; charset=gb2312">
</head>
<body bgcolor="#FFFFFF" background="IMAGE/di.gif">
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td>
<p style="line-height: 200%" align="center"><b><font size="5">偏序关系</font></b> </p>
<p style="line-height: 200%"><b>一、定义</b> </p>
<p style="line-height: 200%"> 设R为P上的二元关系，若R是自反的、反对称的和可传递的，则称R是P上的一个偏序关系。记为：<img border="0" src="Image/xiaodeng.gif" width="9" height="10">
，或用序偶<P,<img border="0" src="Image/xiaodeng.gif" width="9" height="10">>称为偏序集。</p>
<p style="line-height: 200%"><b>例1：</b>自然数集合N上“小于等于”关系是偏序关系。</p>
<p style="line-height: 200%">证明：<br>
(1)任何自然数a,都有a <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
a, 即满足自反性.<br>
(2)<img border="0" src="Image/renyi.gif" width="9" height="11">x,y<img border="0" src="Image/shuyu.gif" width="13" height="11">N,若x
<img border="0" src="Image/xiaodeng.gif" width="9" height="10"> y,y <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
x 则x=y,即满足反对称性.<br>
(3)<img border="0" src="Image/renyi.gif" width="9" height="11">x,y,z<img border="0" src="Image/shuyu.gif" width="13" height="11">N,若x
<img border="0" src="Image/xiaodeng.gif" width="9" height="10"> y,y <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
z 则 x <img border="0" src="Image/xiaodeng.gif" width="9" height="10"> z,即满足传递性.<br>
所以 <N,<img border="0" src="Image/xiaodeng.gif" width="9" height="10">
>为偏序关系.</p>
<p style="line-height: 200%"><b>例2:</b>设P={2,3,4,6,8},<img border="0" src="Image/xiaodeng.gif" width="9" height="10">={<x,y>|
x|y},验证<P,<img border="0" src="Image/xiaodeng.gif" width="9" height="10">>是偏序关系。</p>
<p style="line-height: 200%"> <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
=
{<2,2>,<2,4>,<2,6>,<2,8>,<3,3>,<3,6>,<br>
<4,4>,<4,8>,<6,6>,<8,8>}</p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"><b>二、Hass图</b></p>
<p style="line-height: 200%"> 偏序集<P,<img border="0" src="Image/xiaodeng.gif" width="9" height="10">>的Hass图的做法:<br>
(1) 以小园点表示P中的每一个元素.<br>
(2) 若x <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
y且x <img border="0" src="Image/buden.gif" width="8" height="8"> y,将代表y的结点画在x的上方.<br>
(3) 若x <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
y且不存在z使得x <img border="0" src="Image/xiaodeng.gif" width="9" height="10"> z,z <img border="0" src="Image/xiaodeng.gif" width="9" height="10">
y,则用直线连接,并省去箭头.</p>
<p style="line-height: 200%"><b>例1:</b>如上例的Hass图可表示成:</p>
<p style="line-height: 200%" align="center"><img border="0" src="Image/gxt13.gif" width="97" height="141"></p>
<p style="line-height: 200%"><b>例2:</b>给定关系的hass图,请给出二元关系.</p>
<p style="line-height: 200%" align="center"><img border="0" src="Image/gxt14.gif" width="187" height="145"></p>
<blockquote>
<p style="line-height: 200%" align="left">R={<a,a>,<a,b>,<a,c>,<a,e>,<a,f>,<b,b>,<br>
<c,c>,<b,e>,<c,f>,<e,e>,<f,f>,<d,d>,<br>
<d,f>,<d,g>,<g,g>,<h,h>}</p>
</blockquote>
<p style="line-height: 200%" align="center"> </p>
<p style="line-height: 200%" align="center"> </p>
<p style="line-height: 200%" align="center"> </p>
<p style="line-height: 200%"> </p>
</td>
</tr>
</table>
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td>
<div align="center">
<p style="line-height: 200%"> <img src="IMAGE/yuancheng_2.gif" width="100" height="69"></div>
</td>
</tr>
</table>
<p style="line-height: 200%" align="center"> </p>
<p style="line-height: 150%"> </p><p align="right"><b><a href="contentFrame-mulu.htm"><<back</a></b>
</body>
</html>
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -