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# 数学代写|离散数学代写Discrete Mathematics代考|CSC226 Using Diagrams to Test for Validity

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## 数学代写|离散数学代写Discrete Mathematics代考|Using Diagrams to Test for Validity

Consider the statement
All integers are rational numbers.
Or, formally,
$\forall$ integer $n, n$ is a rational number.
Picture the set of all integers and the set of all rational numbers as disks. The truth of the given statement is represented by placing the integers disk entirely inside the rationals disk, as shown in Figure 3.4.1.

Because the two statements ” $\forall x \in D, Q(x)$ ” and ” $\forall x$, if $x$ is in $D$ then $Q(x)$ ” are logically equivalent, both can be represented by diagrams like the foregoing.

Perhaps the first person to use diagrams like these to analyze arguments was the German mathematician and philosopher Gottfried Wilhelm Leibniz. Leibniz (LIPE-nits) was far ahead of his time in anticipating modern symbolic logic. He also developed the main ideas of the differential and integral calculus at approximately the same time as (and independently of) Isaac Newton (1642-1727).

To test the validity of an argument diagrammatically, represent the truth of both premises with diagrams. Then analyze the diagrams to see whether they necessarily represent the truth of the conclusion as well.

## 数学代写|离散数学代写Discrete Mathematics代考|Using a Diagram to Show Validity

Use diagrams to show the validity of the following syllogism:
All human beings are mortal.
Zeus is not mortal.
$\therefore$ Zeus is not a human being.
Solution The major premise is pictured on the left in Figure 3.4.2 by placing a disk labeled “human beings” inside a disk labeled “mortals.” The minor premise is pictured on the right in Figure 3.4.2 by placing a dot labeled “Zeus” outside the disk labeled “mortals.”

The two diagrams fit together in only one way, as shown in Figure 3.4.3.

Since the Zeus dot is outside the mortals disk, it is necessarily outside the human beings disk. Thus the truth of the conclusion follows necessarily from the truth of the premises. It is impossible for the premises of this argument to be true and the conclusion false; hence the argument is valid.
Using Diagrams to Show Invalidity
Use a diagram to show the invalidity of the following argument:
All human beings are mortal.
Felix is mortal.
$\therefore$ Felix is a human being.

## 数学代写|离散数学代写Discrete Mathematics代考|使用图表来测试有效性

$对于所有$整数$n，$是一个有理数。

## 数学代写|离散数学代写Discrete Mathematics代考|用图示来显示有效性

$因此$ 宙斯不是人。

$因此$菲利克斯是一个人。

## 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。