Tarea 5
Forfatter:
larry061198
Sidst opdateret:
8 år siden
Licens:
Creative Commons CC BY 4.0
Resumé:
TABLA EQUIVALENCIAS CUANTIFICADORES
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
TABLA EQUIVALENCIAS CUANTIFICADORES
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
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\begin{document}
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{\centering\LARGE\bf \thetitle}
Larry Murcia Terranova
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\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
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