Tarea 5
Author:
larry061198
Last Updated:
před 8 lety
License:
Creative Commons CC BY 4.0
Abstract:
TABLA EQUIVALENCIAS CUANTIFICADORES
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
TABLA EQUIVALENCIAS CUANTIFICADORES
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[12pt]{article}
% packages
\usepackage[spanish,activeacute]{babel}
\usepackage[latin1]{input enc}
\usepackage[abs]{overpic}
\usepackage[vflt]{floatflt}
\usepackage{geometry} % Flexible and complete interface to document dimensions
\usepackage[T1]{fontenc} % Standard package for selecting font encodings
\usepackage{fancyhdr} % Extensive control of page headers and footers in LaTeX2ε % Control layout of itemize, enumerate, description
\usepackage{hyperref} % Extensive support for hypertext in LaTeX
\usepackage{titling} % Control over the typesetting of the \maketitle command
\usepackage{natbib} % Flexible bibliography support
\usepackage{mathtools} % Mathematical tools to use with amsmath
\usepackage{titlesec} % Select alternative section titles
\usepackage{lastpage} % Reference last page for Page N of M type footers
\usepackage{amsmath} % AMS mathematical facilities for LaTeX
\usepackage{amsfonts} % TeX fonts from the American Mathematical Society
\usepackage{amssymb} % Additional symbols from American Mathematical Society
\usepackage{wasysym} % LaTeX support file to use the WASY2 fonts
\usepackage{stmaryrd} %Define double brackets
\usepackage{bbm} % "Blackboard-style" cm fonts
\usepackage{array} % Extending the array and tabular environments
\usepackage{xr} % References to other LaTeX documents
\usepackage{verbatim} % Reimplementation of and extensions to LaTeX verbatim
\usepackage{float} % Improved interface for floating objects
\usepackage{multirow} % Allow you to join rows but no idea about columns
\pagenumbering{arabic}
\def\R{\mathbb{R}}
\def\N{\mathbb{N}}
% : set options
% : set `geometry` options
% `letterpaper` is equivalent to `size={8.5in,11in}`
\geometry{letterpaper,margin=1in}
% : set `hyperref' options
\hypersetup{%
pdfborderstyle={/S/U/W 1}% border style will be underline of width 1pt
}
% : set bibliography style
\setcitestyle{round,numbers}
\bibliographystyle{CSE}
% : set the line spacing
\linespread{1.5}
% : set header and footer style
\pagestyle{fancy}
% ======================================================================
% : (re)define LaTeX macros
% : hide section numbering
\titleformat{name=\section}{\normalfont\Large\bfseries}{}{0pt}{}
\titleformat{name=\subsection}{\normalfont\large\bfseries}{}{0pt}{}
\titleformat{name=\subsubsection}{\normalfont\normalsize\bfseries}{}{0pt}{}
% : define `optincludegraphics` custom command
% : toggle including graphics in the manuscript
% : do not include graphics
\newcommand{\optincludegraphics}[2][]{}
% : include graphics
% \newcommand{\optincludegraphics}[2][{}]{\includegraphics[{#1}]{{#2}}}
% : define `optinput` custom command
% : toggle including files (including tables) in the manuscript
% : do not include tables
\newcommand{\optinput}[1]{}
% : include tables
% \newcommand{\optinput}[1]{\input{#1}}
% : define `capt` custom command
% : facilitate use of a title caption
% : usage: \capt[<caption-title>}]{<caption-text>}
\newcommand{\capt}[2][]{\caption[{#1}]{\textbf{{#1}}\newline{#2}}}
% : fix format of references' list
\renewcommand{\bibnumfmt}[1]{#1}
% : fix format of equations
\newtagform{brackets}{[}{]}
\usetagform{brackets}
% : define Taller names, variables, others
\newcommand{\thejournal}[0]{L\'ogica Para Ciencia De La Computaci\'on}
\newcommand{\subtitle}[0]{Tarea 5}
\newcommand{\val}[0]{\textit{v}}
\newcommand{\Le}[0]{L_{\Sigma}}
\newcommand{\Al}{A_{\Sigma}}
\newcommand{\Alf}{A_{\Sigma}^{*}}
\newcommand{\pu}{\varphi_{1}}
\newcommand{\pd}{\varphi_{2}}
\newcommand{\letra}{\mathcal{L}}
\newcommand{\cj}{\varPhi}
\newcommand{\pro}{pf(\varphi)}
\newcommand{\cone}{cn(\varphi)}
% ======================================================================
% : set the title
%TC:ignore
%FIXME
\title{\thejournal}
%TC:endignore
% ======================================================================
% : set header and footer appearance
\renewcommand{\sectionmark}[1]{\markright{#1}}
\newcommand{\sectioname}{\nouppercase{\rightmark}}
% : header
\lhead{\small }
\chead{\small }
\rhead{\small \textsc{\subtitle}}
% : footer
\lfoot{}
\cfoot{}
\rfoot{\thepage\ / \pageref{LastPage}}
% ======================================================================
\begin{document}
%TC:ignore
\begin{titlepage}
{\centering\LARGE\bf \thetitle}
Larry Murcia Terranova
%\bigskip
\end{titlepage}
% Resize BoxTable
\begin{center}
\begin{tabular}[c]{|c|c|}
\hline
\multirow{2}{8cm}{Cuantificaciones Sin Efecto} & $\exists x \ \varphi \ \equiv \ \varphi$ \ \ si $x\notin lib(\varphi) $ \\
& $\forall x \ \varphi \ \equiv \ \varphi$ \ \ si $x\notin lib(\varphi)$ \\
\hline
\multirow{2}{8cm}{Cuantificaciones Sucesivas} & $\exists x \exists y \ \varphi \ \equiv \ \exists y \exists x \ \varphi$ \\
& $\forall x \forall y \ \varphi \ \equiv \ \forall y \forall x \ \varphi$ \\
\hline
\multirow{2}{8cm}{Negaci\'on De Cuantificaciones} & $\lnot\forall x \ \varphi \ \equiv \ \exists x \ \lnot\varphi$ \\
& $\lnot\exists x \ \varphi \ \equiv \ \forall x \ \lnot\varphi$ \\
\hline
\multirow{6}{8cm}{Cuantificaci\'on Conjunci\'on y Disyunci\'on} & $\exists x \ \varphi \vee \exists x \ \Psi \ \equiv \ \exists x \ (\varphi \vee \Psi)$ \\
& $\forall x \ \varphi \wedge \forall x \ \Psi \ \equiv \ \forall x \ (\varphi \wedge \Psi)$ \\
& $\exists x \ \varphi \vee \Psi \ \equiv \ \exists x \ (\varphi \vee \Psi)$ \ \ si $x \notin lib(\Psi)$ \\
& $\exists x \ \varphi \wedge \Psi \ \equiv \ \exists x \ (\varphi \wedge \Psi)$ \ \ si $x \notin lib(\Psi)$ \\
& $\forall x \ \varphi \vee \Psi \ \equiv \ \forall x \ (\varphi \vee \Psi)$ \ \ si $x \notin lib(\Psi)$ \\
& $\forall x \ \varphi \wedge \Psi \ \equiv \ \forall x \ (\varphi \wedge \Psi)$ \ \ si $x \notin lib(\Psi)$ \\
\hline
\multirow{4}{8cm}{Cuantificadores En Condicionales} & $\exists x \ \varphi\Rightarrow\Psi \ \equiv \ \forall x \ (\varphi\Rightarrow\Psi)$ \ \ si $x \notin lib(\Psi)$ \\
& $\forall x \ \varphi\Rightarrow\Psi \ \equiv \ \exists x \ (\varphi\Rightarrow\Psi)$ \ \ si $x \notin lib(\Psi)$ \\
& $\varphi\Rightarrow\exists x \ \Psi \ \equiv \ \exists x (\varphi\Rightarrow\Psi)$ \ \ si $x \notin lib(\varphi)$ \\
& $\varphi\Rightarrow\forall x \ \Psi \ \equiv \ \forall x (\varphi\Rightarrow\Psi)$ \ \ si $x \notin lib(\varphi)$ \\
\hline
\multirow{2}{8cm}{Renombramiento De Variable} & $\exists x \ \varphi \ \equiv \ \exists y \ \varphi_{[x/y]}$ \ \ si $y\neq x$ \ y \ $y \notin lib(\varphi)$ \\
& $\forall x \ \varphi \ \equiv \ \forall y \ \varphi_{[x/y]}$ \ \ si $y\neq x$ \ y \ $y \notin lib(\varphi)$ \\
\hline
\end{tabular}
\end{center}
\end{document}
=====================================================================