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# 数学代写|离散数学代写Discrete Mathematics代考|MAT2520 Valid and Invalid Arguments

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## 数学代写|离散数学代写Discrete Mathematics代考|Valid and Invalid Arguments

“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.” – Lewis Carroll, Through the Looking Glass
In mathematics and logic an argument is not a dispute. It is simply a sequence of statements ending in a conclusion. In this section we show how to determine whether an argument is valid-that is, whether the conclusion follows necessarily from the preceding statements. We will show that this determination depends only on the form of an argument, not on its content.

It was shown in Section $2.1$ that the logical form of an argument can be abstracted from its content. For example, the argument
If Socrates is a man, then Socrates is mortal.
Socrates is a man.
$\therefore$ Socrates is mortal.
has the abstract form
If $p$ then $q$
$\quad p$
$\therefore q$
When considering the abstract form of an argument, think of $p$ and $q$ as variables for which statements may be substituted. An argument form is called valid if, and only if, whenever statements are substituted that make all the premises true, the conclusion is also true.

## 数学代写|离散数学代写Discrete Mathematics代考|Determining Validity or Invalidity

Determine whether the following argument form is valid or invalid by drawing a truth table, indicating which columns represent the premises and which represent the conclusion, and annotating the table with a sentence of explanation. When you fill in the table, you only need to indicate the truth values for the conclusion in the rows where all the premises are true (the critical rows) because the truth values of the conclusion in the other rows are irrelevant to the validity or invalidity of the argument.
\begin{aligned} p & \rightarrow q \vee \sim r \ q & \rightarrow p \wedge r \ \therefore p & \rightarrow r \end{aligned}
Solution The truth table shows that even though there are several situations in which the premises and the conclusion are all true (rows 1,7 , and 8), there is one situation (row 4) where the premises are true and the conclusion is false.

## 数学代写|离散数学代写离散数学代考|有效和无效的参数

.

“恰恰相反，”特威帝继续说，“如果是这样，那就可能是这样;如果是这样，那就会是这样;但既然不是，那就不是。这就是逻辑。”-刘易斯·卡罗尔《镜中奇遇记》

$\therefore$苏格拉底是凡人。

$\quad p$
$\therefore q$

## 数学代写|离散数学代写离散数学代考|判断有效性或无效

.

\begin{aligned} p & \rightarrow q \vee \sim r \ q & \rightarrow p \wedge r \ \therefore p & \rightarrow r \end{aligned}

## 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。