离散结构和离散数学中文书_在离散数学中对场景执行的操作

离散结构和离散数学中文书

Prerequisite: Set theory and types of set in Discrete Mathematics

先决条件： 离散数学中的集合论和集合类型

集的基数 (Cardinality of set)

It is the number of elements in a set denoted like, A= {1, 2, 3, 4}

它是集合中元素的数量，表示为A = {1,2,3,4}

    |A| = 4  | | symbol of cardinality

集合的标准符号 (Standard notations of set)

There are many notations which are used in the set.

集合中使用了许多符号。

C = set of all complex number that can be represented in form of a+ib, a, b are real number.
C =可以以+ ib ， a，b形式表示的所有复数的集合。
R = set of all real number that is represented along a line.
R =沿一条线表示的所有实数的集合。
Q = set of all rational number that can be expression.
Q =可以表示的所有有理数的集合。
Z = set of all integer.
Z =所有整数的集合。
Number without fractional components.
没有小数部分的数字。
W = set of all whole number. Set of all positive (integer) and zero.
W =整数的集合。设置所有正数(整数)和零。
N = Non negative number.
N =非负数。

集的建设 (Construction of set)

A set can be represented by two methods:

一个集合可以用两种方法表示：

Tabulation/Roster method
制表/公鸡法

In the tabulation method, we describe a set by actually writing every number of the set. In this method, we prepare a list of objects forming the set writing the elements one after another between a pair of curly brackets. Thus a set a whose elements are
在制表方法中，我们通过实际写入集合的每个数字来描述集合。在这种方法中，我们准备了一个对象列表，该对象列表构成了一组在一对大括号之间一个接一个地写元素的集合。因此，一个集合的元素是

1, 3, 5,... will be written as A = {1, 3, 5, ...}.
1，3，5，...将被写为A = {1，3，5，...} 。
Set builder
集构建器

In this, we describe a set by actually writing the member of set the properties based on which reader can understand what is the set.
在本文中，我们通过实际编写set的成员属性来描述一个set，使读者可以理解什么是set。

A = { x: x E Z 0<x<5 }
A = {x：x EZ 0 <x <5}

集合运算 (Operations of set)

There are many operations which are performed on the set:

在设备上执行许多操作：

1. Union of set

1.集合的并集

For any two set A and B, the union of A and B written as AUB is the set of all elements which are members of the set A or the set B or both, Symbolically it is written as: A U B = { x:x E A or X E B }

对于任何两个集合A和B，用AUB表示的A和B 的并集是集合A或集合B或集合B的成员的所有元素的集合，符号表示为： AUB = {x：x EA或XEB}

Example:

例：

    
Let, A= {1, 2, 3, 4}
B = { 2, 4, 6, 8, 10}
Then , A U B = {1, 2, 3, 4, 5, 6, 7, 8, 10}

2. Intersection of set

2.集合的交集

The intersection of two set A and B denoted A intersection B is the set of elements which belongs to both A and B, it is written as: A intersection B = { x:x E A and xEB}

表示为A的两个集合A和B 的交集A交集B是同时属于A和B的元素集，其写为： 交集B = {x：x EA和xEB}

3. Difference of two set

3.两组差异

The difference of two sets A and B in that order is the set of elements which belongs to A, but which O does not belong to B. We denote the difference of A and B by: A – B or A ~ B

两组A和B的顺序不同之处是属于A的元素集，但是O不属于B的元素集。我们用以下方式表示A和B的差异： A – B或A〜B

Which reads as "A difference B" or "A minus B" symbolically A - B = {x:x E A and X does not belong to B}

读作符号为“ A差B”或“ A减B”的 A-B = {x：x EA，X不属于B}

A ~ B is also called the compliment of B with respect to A.

A〜B也被称为B对A的补充。

Example:

例：


let,A = {a, b, c, d, e}
B= {f, b, d, g}
A – B = {a, c, e}
B – a = {f.g}
A – B does not equal to B – A.

4. Complement of set

4.补集

If U is a universal set containing A then U-A is called the complement of A and is denoted by A' or Ac thus
A' = U – A = {x:x E U and x does not belongs to U}
A' = { x:x does not belong to A}

如果U是包含A的通用集合，则UA称为A的补数，并用A'或Ac表示，因此
A'= U – A = {x：x EU并且x不属于U}
A'= {x：x不属于A}

Example:

例：

    
let,    U  = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A  = {2, 4, 6, 8, 9}
then    A' = {1, 3, 5, 7}

5. Symmetric difference

5.对称差异

If A and B are two sets we define their symmetric difference as the set of all elements that belong to A or to B but not to both A and B and we denote it by (A - B)U(B – A).

如果A和B两组我们定义他们的对称差作为设定属于一个或B但不是以A和B两者的所有元素的和我们通过(A - B)表示它U(乙- A)。