Question: Using LATEX code is down below. i want to fix what is wrong so that it will give me this exact output . My code
Using LATEX code is down below. i want to fix what is wrong so that it will give me this exact output . My code to fix is at the bottom so that i obtain thje exact output. I always ratE MY ANSWER
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\documentclass[10pt]{article}
\usepackage{amsmath, amssymb, amsfonts, bm, latexsym}
\setlength{\textwidth}{7.5in} \setlength{\oddsidemargin}{-.50in} \setlength{\evensidemargin}{-.50in} \textheight 9.75in \topmargin -0.25in \setlength{\parindent}{0in} \pagestyle{empty} %page number in heading, foot empty
\begin{document}
\vspace{.25in}
This file is based on the answer key to a Math 310 Practice Exam.
\begin{enumerate}
\item Use truth tables to determine whether or not the following pairs of statements are logically equivalent. \begin{enumerate} \item $\left[\left(p \land q ight) ightarrow r ight]$ and $\left(p ightarrow r ight) \land \left(q ightarrow r ight)$
\vspace{.1in}
\begin{tabular}{c c}
\begin{minipage}{3.25in}
\begin{tabular}{|c|c|c|c|c|}
\hline
$p$ & $q$ & $r$ & $p \land q$ & $(p \land q) ightarrow r$ \\
\hline
$T$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$T$ & $T$ & $F$ & $T$ & $F$ \\
\hline
$T$ & $F$ & $T$ & $F$ & $T$ \\
\hline
$T$ & $F$ & $F$ & $F$ & $T$ \\
\hline
$F$ & $T$ & $T$ & $F$ & $T$ \\
\hline
$F$ & $T$ & $F$ & $F$ & $T$ \\
\hline
$F$ & $F$ & $T$ & $F$ & $T$ \\
\hline
$F$ & $F$ & $F$ & $F$ & $T$ \\
\hline
\end{tabluar}
&
\begin{minipage}{3.5in}
\begin{tabular}{|c|c|c|c|c|)
\hline
$p$ & $q$ & $r$ & $p ightarrow r$ & $q ightarrow r$ & $(p ightarrow r) \land (q ihgtarrow r)$\\
\hline
$T$ & $T$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$T$ & $T$ & $F$ & $F$ & $F$ & $F$ \\
\hline
$T$ & $F$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$T$ & $F$ & $F$ & $F$ & $T$ & $F$ \\
\hline
$F$ & $T$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$F$ & $T$ & $F$ & $T$ & $F$ & $F$ \\
\hline
$F$ & $F$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$F$ & $F$ & $F$ & $T$ & $T$ & $T$ \\
\hline
\end{minipage}
\\
\end{tabular}
\vspace{.1in}
Since the last columns of there truth tables are not identical, these two propositions are not logically equivalent.
\vspace{.25in}
\item $p \land \left(q \lor r ight)$ and $\left(p \land q ight) \lor \lft(p \land r ight)
\vspace{.1in}
\hspace{-.15in} \begin{tabular}{c c}
\begin{minipage}{3.0in)
\begin{tabular}{|c|c|c|c|c|}
\hline
$p$ & $q$ & $r$ & $q \lor r$ & $p \land (q \lor r)$ \\
\hline
$T$ & $T$ & $T$ & $T$ & $T$ \\
\hline
$T$ & $T$ & $F$ & $T$ & $T$ \\
\hline
$T$ & $F$ & $T$ & $T$ & $T$ \\
\hline
$T$ & $F$ & $F$ & $F$ & $F$ \\
\hline
$F$ & $T$ & $T$ & $T$ & $F$ \\
\hline
$F$ & $T$ & $F$ & $T$ & $F$ \\
\hline
$F$ & $F$ & $T$ & $T$ & $F$ \\
\hline
$F$ & $F$ & $F$ & $F$ & $F$ \\
\hline
\end{tabluar}
\end{minipage}
&
\begin{minipage}{3.35}
\begin{tabular}{|c|c|c|c|c|c|c}
\hline
$p$ & $q$ & $r$ & $p \land q$ & $p \land r$ & $(p \land q) \lor (p \land r)$\\
\hline
$T$ & $T$ & $T$ & $T$ & $T$ & $T$
$T$ & $T$ & $F$ & $T$ & $F$ $T$ \\
\hline
$T$ & $F$ & $T$ & $F$ & $T$ & $T$ \\
\hline
$T$ & $F$ & $F$ & $F$ & $F$ & $F$
\hline
$F$ & $T$ & $T$ & $F$ & $F$ & $F$ \\
\hline
$F$ & $T$ & $F$ & $F$ & $F$ & $F$ \\
\hline
$F$ & $F$ & $T$ & $F$ & $F$ & $F$ \\
\hline
$F$ & $F$ & $F$ & $F$ & $F$ & $F$ \\
\hline
\end{tabular}
\end{minipage}
\\
\end{tabular}
\vspace{.1in}
Since the last columns of there truth tables are identical, these two propositions are logically equivalent.
\end{enumeate}
\end{enumerate}
;;;
This file is based on the answer key to a Math 310 Practice Exam. 1. Use truth tables to determine whether or not the following pairs of statements are logically equivalent. (a) (pA g) r] and (p r) A T F T T Since the last columns of there truth tables are not identical, these two propositions are not logically equivalent. V r) a T T F T F T F F Since the last columns of there truth tables are identical, these two propositions are logically equivalent
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