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# 数学代写|离散数学代写Discrete Mathematics代考|MATH271 Propositional Equivalences

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## 数学代写|离散数学代写Discrete Mathematics代考|Propositional Equivalences

It is sometimes important to replace a logical statement with an equivalent statement in a mathematical argument. One method to determine whether two compound propositions are equivalent is to use well-known logical identities to establish new logical identities. This method is quite effective, especially when there are a large number of propositional variables involved. Table $1.12$ presents some important logical equivalences involving the negation, conjunction, and disjunction operators. Of all logical equivalences, De Morgan’s laws are of great importance, as they have wide applications in logic. De Morgan’s laws state that (1) the negation of an “and” statement is logically equivalent to the “or” statement in which each component is negated, and (2) the negation of an “or” statement is logically equivalent to the “and” statement in which each component is negated.

Table $1.13$ presents some important logical equivalences involving conditional and biconditional statements.

## 数学代写|离散数学代写Discrete Mathematics代考|Logic Puzzles

Logic puzzles require solutions that are based on logical reasoning. A logic puzzle is a problem that can be solved through deductive reasoning. The fact that if an assumption leads to a contradiction and that assumption must be false forms the basis for solving many logic puzzles by eliminating contradictory answers.
Example $1.20$
Knights and Knaves is a type of logic puzzle with two types of people, where knights can only answer questions truthfully (always tell the truth) and knaves can only answer questions falsely (always lie). On the island of knights and knaves, you come to a fork in the road with one individual standing before each path. You know that one of them is a knight, and the other is a knave. You also know that one path leads to freedom, and the other path leads to certain death. You can ask one of the individuals one yes-no question. What do you ask to determine the path to freedom?
Solution
It is important to note there is no need to figure out which person is a knight and which one is a knave to figure out which path leads to freedom. There are several ways to find out which way leads to freedom. One possible question is “Would the other individual tell me that your path leads to freedom?” With this question, the knight will tell the truth about a lie, while the knave will tell a lie about the truth. Therefore the given answer will always be the opposite of the correct one.

## 数学代写|离散数学代与Discrete Mathematics代考|Logic Puzzles

Knights and Knaves 是一种逻辑谜题，有两种类型的人，骑士只能如实回答问题（总是说真

## 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。