Add beginning lecture

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Blizzard Finnegan 2022-01-11 13:42:04 -05:00
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**/*blizzardfinnegan*
**/*.aux
**/*.fdb_latexmk
**/*.fls
**/*.log
**/*.gz
**/*.pdf

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% File: 11-01-2022.tex
% Created: 12:27:17 Tue, 11 Jan 2022 EST
% Last Change: 12:27:17 Tue, 11 Jan 2022 EST
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{soul}
%\usepackage[smartEllipses,hashEnumerators,hybrid]{markdown}
\usepackage{geometry}
\usepackage{dirtytalk}
\usepackage{lplfitch}
\geometry{portrait, margin=1in}
\date{01/11/2022}
\title{%
Introductory Lecture\\
\large MATH--190--04: Discrete Math for Computing}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
Homework is done in WebWork (linked on MyCourses). Quizzes are based on the
homework.
\section{Foundations: Logic}
Deductive logic: Reasoning from premise(s) to conclusion.
The form of an argument is distinguished from its content.
In other words, the same thing that was done in Symbolic Logic (PHIL-205).
\subsection{Connectives}
Reminder:
\begin{itemize}
\item $\neg$ is logical \verb|NOT|.
\item $\land$ is logical \verb|AND|. Note that "but" in English also applies
here.
\item $\lor$ is logical \verb|OR|.
\item $\to$ is logical \verb|IF|, or, in English, "implies".
\item $\leftrightarrow$ is logical \verb|IFF|, or, in english "If and only if".
\item $\oplus$ is logical \verb|XOR|.
\end{itemize}
Remember, overusing paretheses is preferred.
Propositions (single letters) are either true or false.
Compound propositions (sentences) are true or false, depending on the components.
Truth tables are a way of finding the truth status of a sentence.
\begin{tabular}{c|c||c}
$p$ & $q$ & $p\land (q\lor \neg p)$\\
\hline
1 & 1 & 1\\
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 0\\
\end{tabular}
The above sentence can be replaced by $p\land q$.
Remember the properties of logic:
\begin{itemize}
\item Commutative
\item Associative
\item Distributive
\item Identity ($p\land T = p$, $p\lor F = p$)
\item Negation ($p\lor \neg p = T$, $p\land \neg p = F$)
\end{itemize}
\hl{New term! $a\in A$ is the same as "a is a subset or within the set A".}
\end{document}