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\begin{center}
{\LARGE L\'{o}gica}
\end{center}

\textbf{Esquemas }deductivos:

Modus Ponendo Ponens $\frac{%
\begin{array}{l}
p\rightarrow q \\ 
p%
\end{array}
}{%
\begin{array}{l}
q%
\end{array}
}$. Doble Negaci\'{o}n $\frac{%
\begin{array}{c}
p%
\end{array}
}{%
\begin{array}{l}
\lnot \lnot p%
\end{array}
}$ $\frac{%
\begin{array}{c}
\lnot \lnot p%
\end{array}
}{%
\begin{array}{l}
p%
\end{array}
}$.

Modus Tollendo Tollens $\frac{%
\begin{array}{l}
p\rightarrow q \\ 
\lnot q%
\end{array}
}{%
\begin{array}{l}
\lnot p%
\end{array}
}$. Regla de Adjunci\'{o}n $\frac{%
\begin{array}{l}
p \\ 
q%
\end{array}
}{%
\begin{array}{l}
p\wedge q%
\end{array}
}$.

Regla de Disjunci\'{o}n $\frac{%
\begin{array}{l}
p\wedge q%
\end{array}
}{%
\begin{array}{c}
p%
\end{array}
},\frac{%
\begin{array}{l}
p\wedge q%
\end{array}
}{%
\begin{array}{c}
q%
\end{array}
}.$

Modus Tollendo Ponens $\frac{%
\begin{array}{l}
p\vee q \\ 
\lnot p%
\end{array}%
}{%
\begin{array}{l}
q%
\end{array}%
}$ \ \ \ \ $\frac{%
\begin{array}{l}
p\vee q \\ 
\lnot q%
\end{array}%
}{%
\begin{array}{l}
p%
\end{array}%
}$. Silogismo hipot\'{e}tico: $\frac{%
\begin{array}{l}
p\rightarrow q \\ 
q\rightarrow r%
\end{array}%
}{%
\begin{array}{l}
p\rightarrow r%
\end{array}%
}.$

Ley de Ejemplificaci\'{o}n Universal (EU) $\frac{%
\begin{array}{l}
\forall x,p\left( x\right)%
\end{array}
}{%
\begin{array}{l}
p\left( a\right)%
\end{array}
}.$

Ley de Generalizaci\'{o}n Universal (GU) $\frac{%
\begin{array}{c}
a\text{ arbitrario} \\ 
\begin{array}{l}
p\left( a\right) 
\end{array}%
\end{array}%
}{%
\begin{array}{l}
\forall x,p\left( x\right) 
\end{array}%
}.$

Ley de Ejemplificaci\'{o}n Existencial (EE) $\frac{%
\begin{array}{l}
\exists x,p\left( x\right)%
\end{array}
}{%
\begin{array}{l}
p\left( a\right)%
\end{array}
}.$

Ley de Generalizaci\'{o}n Existencial (GE) $\frac{%
\begin{array}{l}
p\left( a\right)%
\end{array}%
}{%
\begin{array}{l}
\exists x,p\left( x\right)%
\end{array}%
}.$

{\large Ejemplos de inferencia.}

\begin{enumerate}
\item {Un mexicano, un ingl\'{e}s y un alem\'{a}n discuten acerca de sus
respectivas materias (L\'{o}gica, Biolog\'{\i}a y Espa\~{n}ol). Usted tiene
estos enunciados:}

\begin{enumerate}
\item El mexicano imparte L\'{o}gica y Espa\~{n}ol.

\item El ingl\'{e}s no imparte Espa\~{n}ol.

\item El ingl\'{e}s imparte una materia distinta a la del alem\'{a}n.

\item El alem\'{a}n imparte Biologia.

Condiciones:\ Uno es falso y los otros 3 verdaderos; los profesores solo
imparten una materia.

Transcribalos a la notaci\'{o}n simb\'{o}lica, escriba una soluci\'{o}n de
que materia imparte respectivamente el mexicano, el ingl\'{e}s y el alem\'{a}%
n y compruebe que su soluci\'{o}n satisface las condiciones impuestas sobre
los enunciados (a), (b), (c) y (d).
\end{enumerate}

\item Traduzca a la notaci{\'{o}}n simb\'{o}lica y demuestre o infiera
(cuando sea posible) los siguientes predicados.

\begin{enumerate}
\item Todos los tiburones son depredadores.

\item Algunas tiburones son peces.

Luego

Algun pez es depredador.
\end{enumerate}

\item Mediante ejemplos y breves argumentos explique como aplica L\'{o}gica
Matem\'{a}tica en la verificaci\'{o}n de correctez de programas de c\'{o}%
mputo.
\end{enumerate}

\end{document}
