Add beginning lecture
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**/*blizzardfinnegan*
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**/*.aux
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**/*.fdb_latexmk
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**/*.fls
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**/*.log
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**/*.gz
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**/*.pdf
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week1/11-01-2022/11-01-2022.tex
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week1/11-01-2022/11-01-2022.tex
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% File: 11-01-2022.tex
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% Created: 12:27:17 Tue, 11 Jan 2022 EST
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% Last Change: 12:27:17 Tue, 11 Jan 2022 EST
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%
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\documentclass[letterpaper]{article}
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\usepackage{amsmath}
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\usepackage{graphicx}
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\usepackage{cancel}
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\usepackage{amssymb}
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\usepackage{listings}
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\usepackage[shortlabels]{enumitem}
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\usepackage{soul}
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%\usepackage[smartEllipses,hashEnumerators,hybrid]{markdown}
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\usepackage{geometry}
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\usepackage{dirtytalk}
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\usepackage{lplfitch}
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\geometry{portrait, margin=1in}
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\date{01/11/2022}
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\title{%
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Introductory Lecture\\
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\large MATH--190--04: Discrete Math for Computing}
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\author{Blizzard MacDougall}
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\begin{document}
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\maketitle
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\pagenumbering{arabic}
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Homework is done in WebWork (linked on MyCourses). Quizzes are based on the
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homework.
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\section{Foundations: Logic}
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Deductive logic: Reasoning from premise(s) to conclusion.
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The form of an argument is distinguished from its content.
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In other words, the same thing that was done in Symbolic Logic (PHIL-205).
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\subsection{Connectives}
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Reminder:
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\begin{itemize}
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\item $\neg$ is logical \verb|NOT|.
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\item $\land$ is logical \verb|AND|. Note that "but" in English also applies
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here.
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\item $\lor$ is logical \verb|OR|.
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\item $\to$ is logical \verb|IF|, or, in English, "implies".
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\item $\leftrightarrow$ is logical \verb|IFF|, or, in english "If and only if".
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\item $\oplus$ is logical \verb|XOR|.
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\end{itemize}
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Remember, overusing paretheses is preferred.
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Propositions (single letters) are either true or false.
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Compound propositions (sentences) are true or false, depending on the components.
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Truth tables are a way of finding the truth status of a sentence.
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\begin{tabular}{c|c||c}
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$p$ & $q$ & $p\land (q\lor \neg p)$\\
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\hline
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1 & 1 & 1\\
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1 & 0 & 0\\
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0 & 1 & 0\\
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0 & 0 & 0\\
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\end{tabular}
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The above sentence can be replaced by $p\land q$.
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Remember the properties of logic:
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\begin{itemize}
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\item Commutative
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\item Associative
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\item Distributive
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\item Identity ($p\land T = p$, $p\lor F = p$)
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\item Negation ($p\lor \neg p = T$, $p\land \neg p = F$)
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\end{itemize}
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\hl{New term! $a\in A$ is the same as "a is a subset or within the set A".}
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\end{document}
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