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# 数学代写|离散数学代写Discrete Mathematics代考|CONDITIONAL

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## 数学代写|离散数学代写Discrete Mathematics代考|CONDITIONAL

Let $\mathrm{P}$ and $\mathrm{Q}$ be any two statements. Then the statement $\mathrm{P} \rightarrow \mathrm{Q}$ is called a conditional statement. This can be put in any one of the following forms.
(a) If $\mathrm{P}$, then $\mathrm{Q}$
(b) P only if $\mathrm{Q}$
(c) P implies $\mathrm{Q}$
(d) $\mathrm{Q}$ if $\mathrm{P}$
In an implication $\mathrm{P} \rightarrow \mathrm{Q}, \mathrm{P}$ is called the antecedent (hypothesis) and $\mathrm{Q}$ is called the consequent (conclusion). To explain the conditional statement, consider the example A boy promises a girl “I will take you boating on Sunday if it is not raining”.
Now if it is raining, then the boy would not be deemed to have broken his promise. The boy would be deemed to have broken his promise only when it is not raining and the boy did not take the girl for boating on Sunday.
Let us break the above conditional statement to symbolic from.
P: It is not raining
Q: I will take you boating on Sunday
So, the above statement reduces to $\mathrm{P} \rightarrow \mathrm{Q}$.
From the above discussion it is clear that if $P$ is false then $P \rightarrow Q$ is true, whatever be the truth value of $Q$. The conditional $P \rightarrow Q$ is false if $P$ is true and $Q$ is false.

Rule: An implication (conditional) $\mathrm{P} \rightarrow \mathrm{Q}$ is False only when the hypothesis $(\mathrm{P})$ is true and conclusion (Q) is false, otherwise True.

## 数学代写|离散数学代写Discrete Mathematics代考|BI-CONDITIONAL

Let $\mathrm{P}$ and $\mathrm{Q}$ be any two statements. Then the statement $\mathrm{P} \leftrightarrow \mathrm{Q}$ is called a bi-conditional statement. This $P \leftrightarrow Q$ can be put in any one of the following forms.
(a) $\mathrm{P}$ if and only if $\mathrm{Q}$
(b) $\mathrm{P}$ is necessary and sufficient of $\mathrm{Q}$
(c) $\mathrm{P}$ is necessary and sufficient for $\mathrm{Q}$
(d) $\mathrm{P}$ is implies and implied by $\mathrm{Q}$
The bi-conditional (double implication) $P \leftrightarrow Q$ is defined as
$$(\mathbf{P} \leftrightarrow \mathbf{Q}):(\mathbf{P} \rightarrow \mathbf{Q}) \wedge(\mathbf{Q} \rightarrow \mathbf{P})$$
From the truth table discussed below it is clear that $P \leftrightarrow Q$ has the truth value $T$ whenever both $\mathrm{P}$ and $\mathrm{Q}$ have identical truth values.

Rule: $(\mathrm{P} \leftrightarrow \mathrm{Q})$ is True only when both $\mathrm{P}$ and $\mathrm{Q}$ have identical truth Values, otherwise false.

Let $\mathrm{P}$ and $\mathrm{Q}$ be any two statements. The converse statement of the conditional $\mathrm{P} \rightarrow \mathrm{Q}$ is given as $\mathrm{Q} \rightarrow \mathrm{P}$.

Consider the example “all concurrent triangles are similar”. The above statement can also be written as “if triangles are concurrent, then they are similar”.
Let $P$ : Triangles are concurrent
Q : Triangles are similar
So, the statement becomes $\mathrm{P} \rightarrow \mathrm{Q}$. The converse statement is given as “if triangles are similar, then they are concurrent” or all similar triangles are concurrent.

## 数学代写|离散数学代写Discrete Mathematics代考|CONDITIONAL

(a)如果$\mathrm{P}$，那么$\mathrm{Q}$
(b) P仅当$\mathrm{Q}$
(c) P表示$\mathrm{Q}$
(d) $\mathrm{Q}$如果$\mathrm{P}$

P:没有下雨

## 数学代写|离散数学代写Discrete Mathematics代考|BI-CONDITIONAL

(a) $\mathrm{P}$当且仅当$\mathrm{Q}$
(b) $\mathrm{P}$是$\mathrm{Q}$的必要和充分条件
(c) $\mathrm{P}$对于$\mathrm{Q}$是必要和充分的
(d) $\mathrm{Q}$暗示和暗示$\mathrm{P}$

$$(\mathbf{P} \leftrightarrow \mathbf{Q}):(\mathbf{P} \rightarrow \mathbf{Q}) \wedge(\mathbf{Q} \rightarrow \mathbf{P})$$

## 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。