離散結構和離散數學中文書

Prerequisite: Set theory and types of set in Discrete Mathematics

先決條件： 離散數學中的集合論和集合類型

集的基數 (Cardinality of set)

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

它是集合中元素的數量，表示為A = {1,2,3,4}

|A| = 4 | | symbol of cardinality

集合的標準符號 (Standard notations of set)

There are many notations which are used in the set.

集合中使用了許多符號。

• 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形式表示的所有復數的集合。

• R = set of all real number that is represented along a line.

  R =沿一條線表示的所有實數的集合。

• Q = set of all rational number that can be expression.

  Q =可以表示的所有有理數的集合。

• Z = set of all integer.

  Z =所有整數的集合。

• Number without fractional components.

  沒有小數部分的數字。

• W = set of all whole number. Set of all positive (integer) and zero.

  W =整數的集合。 設置所有正數(整數)和零。

• N = Non negative number.

  N =非負數。

集的建設 (Construction of set)

A set can be represented by two methods:

一個集合可以用兩種方法表示：

Tabulation/Roster method

制表/公雞法

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，我們通過實際寫入集合的每個數字來描述集合。 在這種方法中，我們準備了一個對象列表，該對象列表構成了一組在一對大括號之間一個接一個地寫元素的集合。 因此，一個集合的元素是

1, 3, 5,... will be written as A = {1, 3, 5, ...}.

1，3，5，...將被寫為A = {1，3，5，...} 。

Set builder

集構建器

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，我們通過實際編寫set的成員屬性來描述一個set，使讀者可以理解什么是set。

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

A = {x：x EZ 0 <x <5}

集合運算 (Operations of set)

There are many operations which are performed on the set:

在設備上執行許多操作：

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 }

對于任何兩個集合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的成員的所有元素的集合，符號表示為： 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}

表示為A的兩個集合A和B 的交集A交集B是同時屬于A和B的元素集，其寫為： 交集B = {x：x EA和xEB}

3. Difference of two set

3.兩組差異

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

兩組A和B的順序不同之處是屬于A的元素集，但是O不屬于B的元素集。 我們用以下方式表示A和B的差異： 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}

讀作符號為“ A差B”或“ A減B”的 A-B = {x：x EA，X不屬于B}

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

A?B也被稱為B對A的補充 。

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.補集

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，則UA稱為A的補數，并用A'或Ac表示，因此
A'= U – A = {x：x EU并且x不屬于U}
A'= {x：x不屬于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.對稱差異

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兩組我們定義他們的對稱差作為設定屬于一個或B但不是以A和B兩者的所有元素的和我們通過(A - B)表示它U(乙- A)。

翻譯自: https://www.includehelp.com/basics/operations-performed-on-the-set-in-discrete-mathematics.aspx

離散結構和離散數學中文書

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