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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|组合学代写Combinatorics代考|Union

The elements of the sets $A$ and $B$ taken together, form the set which is called the union of the sets $A$ and $B$ and is denoted by $A \cup B$. That is
$$A \cup B={x \mid x \in A \text { or } x \in B} .$$
It is necessary to make two remarks here.

1. According to the definition of a set, every element of a set is unique. There can be no two identical elements in a set. In particular, if sets $A$ and $B$ have common elements $(A \cap B \neq \emptyset)$, then each such element is presented in the union $A \cup B$ of these sets by only one element.
2. The conjunction “or” in English, as well as its correspondences in other languages, is used in two different contexts. “Would you like coffee with milk or black coffee”, “It will be raining or dry”, “You should wear boots or shoes to enter the restaurant”, “We plant rye or wheat in this area in autumn” – in all these phrases the conjunction “or” is used to suggest that only one possibility can be realized. In other words, in the above cases, the conjunction “or” combines alternative, incompatible options. However, sometimes this conjunction provides another, completely different meaning. “We hire for the positions of translators and assistants anyone who speaks German or French”. There is no chance that someone will understand this announcement as if it only refers to those who speak only one of the two languages. The employer will gladly hire those who speak both languages. So, here the conjunction “or” is used in a different sense compared to the preceding examples. These two meanings can be called segregating and non-segregating respectively. The latter meaning is the one that is inherent in the definition of the union of sets $A$ and $B$, expressed by formula (2.1). This definition should be understood as follows. An element $x$ is included in $A \cup B$ in three cases, namely: when it belongs to $A$ and not to $B$; when it belongs to $B$ and not to $A$; and finally, when it belongs to both of these sets, that is, to their intersection. It is appropriate to illustrate the above by a schematic drawing (see Fig. 2.1).

Two circles depict the sets $A$ and $B$. Their common part, looking like a biconvex lens, depicts an intersection $A \cap B$ (in the figure this part is crosshatched). The whole shaded figure made up of two crescents and a lens, corresponds to the union $A \cup B$. Schematic drawings used to illustrate the operations with sets are called the Euler diagrams (Eulerian circles) after the Swiss mathematician of the XVIII century, one of the most prominent creators of modern mathematics.
Below, we provide several examples illustrating the notion of union of sets.

## 数学代写|组合学代写Combinatorics代考|Difference

The difference of $A$ and $B$ (also called the set-theoretic difference of $A$ and $B$, or relative complement of $B$ with respect to $A)$, denoted by $A \backslash B$, is the set of all elements that are members of $A$ but are not members of $B$. Thus,
$$A \backslash B={x \mid x \in A, x \notin B} .$$
In order to get the set $A \backslash B$, one needs to remove from the set $A$ all those elements, which belong to $B$. On the Euler diagram Fig. $2.1$ the set $A \backslash B$ is a shaded crescent. If $A \cap B=0$, then naturally $A \backslash B=A$.

Example 2.14. Let $A$ be the set of all straight lines in space, let l be one of these lines, and let $B$ be the set of those lines in space, which lay in the same plane with $l$. In other words, a line $t$ belongs to $B$ if and only if there exists a plane, containing $t$ and $l$. In this case, $A \backslash B$ consists of lines, which are skew to the line l, and $B \backslash A$ is an empty set.

Example 2.15. If $N_3$ is the set of those natural numbers, which are divisible by $3, N_2$ is the set of even natural numbers, then $N_3 \backslash N_2$ is the set of all those odd natural numbers, which are divisible by 3 , and $N_2 \backslash N_3$ is the set of those even natural numbers, which are not divisible by 3.

Example 2.16. Let A be the set of those three-digit natural numbers, which have at least one even digit, and $B$ be the set of those three-digit natural numbers, which have at least one odd digit. Then $A \backslash B$ is the set of all those three-digit numbers, all digits of which are even, and $B \backslash A$ is the set of all those three-digit numbers, all digits of which are odd.
Example 2.17. The difference $R \backslash Q$ is the set of irrational numbers.

# 组合学代考

## 数学代写|组合学代写Combinatorics代考|Union

1. 根据集合的定义，集合的每个元素都是唯一的。一个集合中不可能有两个相同的元素。特别是，如果集一个和乙有共同的元素(一个∩乙≠∅), 然后每个这样的元素都出现在并集中一个∪乙这些集合中只有一个元素。
2. 英语中的连词“或”，以及它在其他语言中的对应，在两种不同的上下文中使用。“你要加牛奶的咖啡还是黑咖啡”、“下雨还是天干”、“你应该穿靴子或鞋子进入餐厅”、“我们秋天在这个地区种植黑麦或小麦”——所有这些短语“或”连词表示只能实现一种可能性。换句话说，在上述情况下，连词“或”结合了替代的、不兼容的选项。然而，有时这个连词提供了另一种完全不同的含义。“我们聘请会说德语或法语的任何人担任翻译和助理的职位”。没有机会有人会理解这个公告，好像它只是指那些只会说两种语言中的一种的人。雇主很乐意雇用会说两种语言的人。因此，与前面的示例相比，这里使用的连词“或”的含义不同。这两种含义可以分别称为隔离和非隔离。后一种含义是集合并集定义中固有的含义一个和乙，用公式（2.1）表示。该定义应理解如下。一个元素X包含在一个∪乙在三种情况下，即：当它属于一个而不是乙; 当它属于乙而不是一个; 最后，当它属于这两个集合时，即属于它们的交集。可以用示意图来说明上述情况（见图 2.1）。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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