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# 数学代写|离散数学代写Discrete Mathematics代考|MATH215 Implicit Quantification

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## 数学代写|离散数学代写Discrete Mathematics代考|Implicit Quantification

Consider the statement
If a number is an integer, then it is a rational number.
As shown earlier, this statement is equivalent to a universal statement. However, it does not contain the telltale word all or every or any or each. The only clue to indicate its universal quantification comes from the presence of the indefinite article $a$. This is an example of implicit universal quantification.

Existential quantification can also be implicit. For instance, the statement “The number 24 can be written as a sum of two even integers” can be expressed formally as ” $\exists$ even integers $m$ and $n$ such that $24=m+n . “$

Mathematical writing contains many examples of implicitly quantified statements. Some occur, as in the first example above, through the presence of the word $a$ or $a$. Others occur in cases where the general context of a sentence supplies part of its meaning. For example, in an algebra course in which the letter $x$ is always used to indicate a real number, the predicate
If $x>2$ then $x^2>4$
is interpreted to mean the same as the statement
For every real number $x$, if $x>2$ then $x^2>4$.
Mathematicians often use a double arrow to indicate implicit quantification symbolically. For instance, they might express the above statement as
$$x>2 \Rightarrow x^2>4$$

## 数学代写|离散数学代写Discrete Mathematics代考|Tarski’s World

Tarski’s World is a computer program developed by information scientists Jon Barwise and John Etchemendy to help teach the principles of logic. It is described in their book The Language of First-Order Logic, which is accompanied by a CD containing the program Tarski’s World, named after the great logician Alfred Tarski.

Investigating Tarski’s World
The program for Tarski’s World provides pictures of blocks of various sizes, shapes, and colors, which are located on a grid. Shown in Figure 3.1.1 is a picture of an arrangement of objects in a two-dimensional Tarski world. The configuration can be described using logical operators and-for the two-dimensional version-notation such as Triangle $(x)$, meaning ” $x$ is a triangle,” $\operatorname{Blue}(y)$, meaning ” $y$ is blue,” and RightOf $(x, y)$, meaning ” $x$ is to the right of $y$ (but possibly in a different row).” Individual objects can be given names such as $a, b$, or $c$.

Determine the truth or falsity of each of the following statements. The domain for all variables is the set of objects in the Tarski world shown in Figure 3.1.1.
a. $\forall t$, Triangle $(t) \rightarrow$ Blue $(t)$.
b. $\forall x$, Blue $(x) \rightarrow$ Triangle $(x)$.
c. $\exists y$ such that Square $(y) \wedge \operatorname{RightOf}(d, y)$.
d. $\exists z$ such that $\operatorname{Square}(z) \wedge \operatorname{Gray}(z)$.

## 数学代写|离散数学代写Discrete Mathematics代考|Implicit Quantification

If $x>2$ 然后 $x^2>4$

$$x>2 \Rightarrow x^2>4$$

## 数学代写|离散数学代写Discrete Mathematics代考|Tarski’s World

Tarski’s World 是由信自科学家 Jon Barwise 和 John Etchemendy 开发的计算机程序，用于邦助教授逻辑原埋。在他们的书 《一阶逻辑语言》中对此进行了描述，该书还阡有一张 CD，其中包含以伟大的逻辑学家阿尔弗雷德.塔斯基命名的程序“塔斯甚的 世眻”。

b. $\forall x$ ，监色的 $(x) \rightarrow$ 三角形 $(x)$.
C。 $\exists y$ 这样广场 $(y) \wedge \operatorname{RightOf}(d, y)$.
d. $\exists z$ 这样Square $(z) \wedge \operatorname{Gray}(z)$.

## 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。