Skip to main content \(\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}}
\newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}}
\newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}}
\newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}}
\newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}}
\newcommand{\Null}{\operatorname{Null}} \renewcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\N}{{\mathbb N}} \newcommand{\Z}{{\mathbb Z}} \newcommand{\Q}{{\mathbb Q}}
\newcommand{\R}{{\mathbb R}} \newcommand{\Zpos}{{{\mathbb Z}^+}} \newcommand{\SUB}{\subseteq}
\newcommand{\SUP}{\supseteq} \newcommand{\PSUB}{\varsubsetneq}
\newcommand{\PSUP}{\varsupsetneq} \newcommand{\SETDIFF}{\smallsetminus}
\newcommand{\st}{\,|\,}
\newcommand{\ab}{\mbox{$\{a,b\}$}} \newcommand{\aetc}[2]{\mbox{{${#1}_1{#1}_2\ldots
{#1}_{#2}$}}} \newcommand{\varep}{\varepsilon}
\newcommand{\fsafig}[1]{\medskip\centerline{\eps{fsa#1}}\medskip}
\newcommand{\REOR}{\hbox{$\,|\,$}} \newcommand{\POW}{{\mathscr P}}
\newcommand{\EMPTYSTRING}{\varepsilon}
\newcommand{\PRODUCES}{\longrightarrow}
\newcommand{\YIELDS}{\Longrightarrow}
\newcommand{\YIELDSTAR}{{\Longrightarrow}^*}
\newcommand{\NT}[1]{\hbox{$\langle$\textit{#1}$\rangle$}}
\newcommand{\BNFPRODUCES}{\hbox{\texttt{::=}}}
\newcommand{\BNFALT}{\hbox{$|$}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 5 Proofs
In this chapter, we will learn to construct valid logical arguments. Although these arguments will usually be applied to mathematics, they employ the same techniques that are used by a lawyer in a courtroom or a physician examining a patient.
