ASSIGNMENT.TEX

\documentclass[12pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{tabular} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \begin{document} \section{Chapter 1 solution} \\ 1) \\ Construct a truth table for each of these compound propositions \begin{description} \item[a)] (p $\wedge$ q) $\rightarrow$ $\neg$q \begin{center} \begin{tabular}{ |c|c|c|c|c| } \hline p & q & $\neg$q & p$\wedge$q & (p$\wedge$q) $\rightarrow$ $\neg$q \\ \hline T & T & F & T & F \\ \hline T & F & T & F & T \\ \hline F & T & F & F & T \\ \hline F & F & T & F & T \\ \hline \end{tabular} \end{center} \item[b)] (p$\vee$r) $\rightarrow$ (r$\vee\neg$p) \begin{center} \begin{tabular}{ |c|c|c|c|c|c| } \hline p & r & $\neg$p & p$\vee$r & r$\vee\neg$p & (p$\vee$r) $\rightarrow$ (r$\vee\neg$p) \\ \hline T & T & F & T & T & T\\ \hline T & F & F & T & F & F\\ \hline F & T & T & T & T & T\\ \hline F & F & T & F & T & T\\ \hline \end{tabular} \end{center} \item[c)] (p$\rightarrow$q) $\vee$ (q$\rightarrow$p) \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline p & q & p$\rightarrow$q & q$\rightarrow$p & (p$\rightarrow$q)$\vee$(q$\rightarrow$p) \\ \hline T & T & T & T & T \\ \hline T & F & F & T & T \\ \hline F & T & T & F & T \\ \hline F & F & T & T & T \\ \hline \end{tabular} \end{center} \item[d)] (p$\vee\neg$q) $\wedge$ ($\neg$p$\vee$q) \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline p & q & $\neg$p & $\neg$q & p$\vee\neg$q & $\neg$p$\vee$q & (p$\vee\neg$q) $\wedge$ ($\neg$p$\vee$q) \\ \hline T & T & F & F & T & T & T \\ \hline T & F & F & T & T & F & F \\ \hline F & T & T & F & F & T & F \\ \hline F & F & T & T & T & T & T \\ \hline \end{tabular} \end{center} \item[e)] (p$\rightarrow\neg$q) $\vee$ (q$\rightarrow\neg$p) \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline p & q & $\neg$p & $\neg$q & p$\rightarrow\neg$q & q$\rightarrow\neg$p & (p$\rightarrow\neg$q) $\vee$ (q$\rightarrow\neg$p) \\ \hline T & T & F & F & F & F & F \\ \hline T & F & F & T & T & T & T \\ \hline F & T & T & F & T & F & T \\ \hline F & F & T & T & T & T & T \\ \hline \end{tabular} \end{center} \item[f)] $\neg$($\neg$p$\wedge\neg$q) \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline p & q & $\neg$p & $\neg$q & $\neg$p$\wedge\neg$q & $\neg$($\neg$p$\wedge\neg$q) \\ \hline T & T & F & F & F & T \\ \hl