Using LATEX code is down below. i want to fix what is wrong so that it will give
ID: 3797216 • Letter: U
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 to fix is at the bottom so that i obtain thje exact output. I always ratE MY ANSWER
;;
documentclass[10pt]{article}
usepackage{amsmath, amssymb, amsfonts, bm, latexsym}
setlength{ extwidth}{7.5in}
setlength{oddsidemargin}{-.50in}
setlength{evensidemargin}{-.50in}
extheight 9.75in
opmargin -0.25in
setlength{parindent}{0in}
pagestyle{empty} %page number in heading, foot empty
egin{document}
space{.25in}
This file is based on the answer key to a Math 310 Practice Exam.
egin{enumerate}
item Use truth tables to determine whether or not the following pairs of statements are logically equivalent.
egin{enumerate}
item $left[left(p land q ight) ightarrow r ight]$ and $left(p ightarrow r ight) land left(q ightarrow r ight)$
space{.1in}
egin{tabular}{c c}
egin{minipage}{3.25in}
egin{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}
&
egin{minipage}{3.5in}
egin{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}
space{.1in}
Since the last columns of there truth tables are not identical, these two propositions are not logically equivalent.
space{.25in}
item $p land left(q lor r ight)$ and $left(p land q ight) lor lft(p land r ight)
space{.1in}
hspace{-.15in} egin{tabular}{c c}
egin{minipage}{3.0in)
egin{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}
&
egin{minipage}{3.35}
egin{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}
space{.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 equivalentExplanation / Answer
Ans is T if T|F=T
F|T=F
TT=T
FF=F
T|F|T|T=T
F|T|F|T=F
If F is True the True else False
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