刚接触 LaTeX，遇到很多错误，不知道如何修复

Question

我今天才开始学习 LaTeX。我尝试以 TeX 格式写一些笔记，但当我尝试构建它时，我遇到了很多错误。你能看看它并找出问题所在吗？谢谢。

\documentclass{article}
\begin{document}
\title{Foundations of CS, Lecture 1}
\author{Ryan}
\date{January 23, 2014}
\maketitle

\textbf{Proposition} - a declarative statement that is either True or False.
\begin{itemize} 
    \item Atomic proposition - basic proposition
    \item Compound proposition - complex proposition that is built upon smaller ones
    \begin{itemize}
        \item Negation - \lnot p
        \item Conjunction - p \land q
        \item Dis-junction - p \lor q
        \item Implication - p \rightarrow q
        \item Bi-conditional - p \longleftrightarrow q
    \end{itemize}
\end{itemize}

For a statement p -> q, there are several related statements:
\begin{itemize}
    \item Converse: q \rightarrow p
    \item Contrapositive: \lnot q \rightarrow \lnot p
    \item Inverse: \lnot p \rightarrow \lnot q
\end{itemize} 

\textbf{Logical Equivalency} - Two propositions are logically equivalent 
if they have the same truth table.
\begin{itemize}
    \item \textbf{Example: }Is p \rightarrow q equivalent to \lnot q \rightarrow \lnot p?
    Truth table goes here
\end{itemize} 

\textbf{Precedence of Logical Operators}
Table goes here

\begin{itemize}
    \item Tautology - proposition that is always True
    \item Contradiction - proposition that is always False
    \item Contingency - proposition that is neither True or False
    \begin{itemize}
        \item For example, p
    \end{itemize}
\end{itemize}       



\end{document}

Answer 1

数学内容需要处于数学模式。一旦我添加 a$以开始数学模式和 a$以结束数学模式，我就会得到：

笔记：

• 你还漏掉了\an 中的a \lnot。除此之外，主要的问题是当你有数学符号时你没有处于数学模式。

• 虽然我使用$进入和退出数学模式，但推荐的方法是使用\(开始数学模式，然后使用\)结束数学模式，如下所示：对于数学模式来说，\( 和 \) 是否比美元符号更可取？。

• 对于您很快就会用到的显示数学，您应该参考为什么 \[ ... \] 比 $$ ... $$ 更可取？。

• 关于数学模式的一个很好的参考是 Herbert Voss 的 对 (La)TeX 中的数学进行全面回顾。

• 根据 Mico 的建议，我已将 替换-为更符合印刷规范的破折号---。请参阅破折号：- 与 – 与 —有关破折号的更多详细信息。我个人建议将其替换为:。

代码：

\documentclass{article}
\begin{document}
\title{Foundations of CS, Lecture 1}
\author{Ryan}
\date{January 23, 2014}
\maketitle

\textbf{Proposition} - a declarative statement that is either True or False.
\begin{itemize} 
    \item Atomic proposition - basic proposition
    \item Compound proposition - complex proposition that is built upon smaller ones
    \begin{itemize}
        \item Negation --- $\lnot p$
        \item Conjunction --- $p \land q$
        \item Dis-junction --- $p \lor q$
        \item Implication --- $p \rightarrow q$
        \item Bi-conditional --- $p \longleftrightarrow q$
    \end{itemize}
\end{itemize}

For a statement $p \to q$, there are several related statements:
\begin{itemize}
    \item Converse: $q \rightarrow p$
    \item Contrapositive: $\lnot q \rightarrow \lnot p$
    \item Inverse: $\lnot p \rightarrow \lnot q$
\end{itemize} 

\textbf{Logical Equivalency} - Two propositions are logically equivalent 
if they have the same truth table.
\begin{itemize}
    \item \textbf{Example: }Is $p \rightarrow q$ equivalent to $\lnot q \rightarrow \lnot p$?
    Truth table goes here
\end{itemize} 

\textbf{Precedence of Logical Operators}
Table goes here

\begin{itemize}
    \item Tautology --- proposition that is always True
    \item Contradiction --- proposition that is always False
    \item Contingency --- proposition that is neither True or False
    \begin{itemize}
        \item For example, $p$
    \end{itemize}
\end{itemize}       

\end{document}