Luis es un buen jugador
Felipe es alegre
Maria hizo la tarea
Jose tiene un globo
Pedro toma agua
Luis es un buen jugador entonces participara en el partido
Felipe es alegre o esta sonriendo por algo mas
Maria hizo la tarea entonces sale a jugar
José tiene un globo y una tarjeta para su novia
Si Pedro toma agua entonces tiene sed
Para todo Luis es un buen jugador
Para todo Felipe es alegre
Para todo Maria hizo la tarea
Para todo Jose tiene un globo
Para todo Pedro toma agua
Para todo Luis es un buen jugador entonces participara en el partido
Para todo Felipe es alegre o esta sonriendo por algo mas
Para todo Maria hizo la tarea entonces sale a jugar
Para todo José tiene un globo y una tarjeta para su novia
Para todo Si Pedro toma agua entonces tiene sed
Existe un Luis que es un buen jugador
Existe un Felipe que es alegre
Existe una Maria que hizo la tarea
Existe un Jose que tiene un globo
Existe un Pedro que toma agua
Existe un Luis que es un buen jugador entonces participara en el partido
Existe un Felipe que es alegre o esta sonriendo por algo mas
Existe un Maria que hizo la tarea entonces sale a jugar
Existe un José que tiene un globo y una tarjeta para su novia
Existe un Pedro que toma agua, entonces tiene sed
¿Que es un sistema logico?
martes, 6 de marzo de 2012
tablas de verdad
P
|
Q
|
R
|
P & Q
|
(P&Q)-> P
|
Q v R
|
¬Q&¬R
|
(QvR)&(¬Q&¬R)
|
[(P&Q)->
P]- >[(QvR)^( ¬Q&¬R)]
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
P
|
Q
|
R
|
P
& Q
|
(P&Q)->
r
|
P
v R
|
[(P&Q)->
r]- > [P v R]
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
P
|
Q
|
R
|
S
|
T
|
U
|
P
& Q
|
P&Q->
r
|
S
& T
|
[(P&Q)->
r] &[S&T]
|
[(P&Q)->
r] &[S&T] -> U
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
P
|
Q
|
R
|
P
& Q
|
(P&Q)->
P
|
Q
v R
|
((P&Q)->
P)-> Q v R
|
¬Q&¬R
|
[(P&Q)->
P]- >[(QvR)]^( ¬Q&¬R)]
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
P
|
Q
|
R
|
¬P
v Q
|
(¬PvQ)->
r
|
P&¬Q
|
(P&¬Q)vR
|
[(¬PvQ)-> r]ó[(P&¬Q)vR]
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
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