Lógica Proposicional

1. MATEMÁTICAS DISCRETAS
LOGICA PROPOSICIONAL TALLER No 1
Yeimi Carolina Acosta Ortiz – 24157
Maryluz Ospina Quintero – 9866
Patricia Olmos - 10090
Jonathan Jair Castro Quiñones – 9829
Omar Urazan García – 9859
Rolando Cuenca -
Universidad ECCI
Bogotá D.C
Sep - 2015

2. •P ˅ q →˜r
•P ˄ q →˜ (p ˄ r)
•˜ p → ˜ r
LOGICA PROPOSICIONAL

4. a.
Contingencia

5. b.
Contingencia

6. Contingencia
c.

7. FNC
(p ˅ ˜ q ˅ r)
FND
(˜p ˄ ˜ q ˄ ˜ r) ˅ (˜p ˄ ˜ q ˄ r) ˅ (˜ p ˄ q ˄ r) ˅ (p ˄ ˜ q ˄ ˜ r) ˅ (p ˄ ˜ q ˄ r) ˅ (p ˄ q ˄ ˜ r) ˅ (p ˄ q ˄ r)
a.

8. FNC
(p ˅ r ˅ s ˅ q) ˄ (p ˅ r ˅ s ˅ ̃q) ˄ (p ˅ r ˅ ̃s ˅ q) ˄ (p ˅ r ˅ ̃s ˅ ̃q) ˄ (p ˅ ̃r ˅ s ˅ q) ˄ (p ˅ ̃ r ˅
s ˅ ̃ q) ˄ (p ˅ ̃ r ˅ ̃ s ˅ q) ˄ (p ˅ ̃ r ˅ ̃ s ˅ ̃ q) ˄ ( ̃ p ˅ r ˅ s ˅ q) ˄ ( ̃ p ˅ r ˅ s ˅ ̃q) ˄ ( ̃p ˅ r
˅ ̃ s ˅ q) ˄ ( ̃p ˅ r ˅ ̃s ˅ ̃q) ˄ ( ̃p ˅ ̃ r ˅ s ˅ q) ˄ ( ̃p ˅ ̃ r ˅ s ˅ ̃ q) ˄ ( ̃ p ˅ ̃ r ˅ ̃ s ˅ q) ˄ ( ̃p
˅ ̃ r ˅ ̃ s ˅ ̃ q)
b.

9. FNC
(p ˅ r ˅ s ) ˄ (p ˅ r ˅ ̃ s ) ˄ ( ̃p ˅ ̃ r ˅ s ) ˄ ( ̃ p ˅ ̃ r ˅ ̃ s )
FND
( ̃ p ˄ r ˄ ̃ s ) ˅ (p ˄ r ˄ s ) ˅ (p ˄ ̃r ˄ ̃ s ) ˅ (p ˄ ̃ r ˄ s )
c.

10. p q r S1 S2 S3
F F F F V F
F F V F F V
F V F V V V
F V V F F V
V F F F V F
V F V V V V
V V F F F F
V V V F F V

11. S1
Disyuntiva
(~p ˄q ˄ r) ˅ (p ˄~q ˄~r)
P˄ ((q˄r) ˅ (~q˄~r))
P˄ (q ↔q)
R PQ 00 01 11 10
0 1
1 1
(~p ˄q ˄ r) ˅ (p ˄~q ˄~r)
P˄ ((q˄r) ˅ (~q˄~r))
P˄ (q ↔q)

12. S2
Disyuntiva
(~p˄~q˄r) ˅ (~p˄q˄r) ˅ (p˄~q˄r) ˅ (p˄~q˄r)
((~p˄r) ˄ (~q˄q) ˅ (p˄~q˄r))
((~p˄r) ˄ (~q˄q) ˅ (p˄~q˄r))
(~p˄r) ˄ (~q˄ (q˅ (p˄r)))
(~p←r) ˄ (~q˄ (q˅ (p˄r)))
R PQ 00 01 11 10
0 1
1 1 1 1
(~q˄r) ˅ (p˄~q) ˅ (~p˄r)

13. S2
Conjuntiva
(p˅q˅~r) ˄ (~p˅q˅~r) ˄ (~p˅~q˅~r)
(p˅q˅~r) ˄ ((~p˅~r) ˅ (q˄~q))
(p˅q˅~r) ˄ ((~p˅~r) ˅ F)
~r ˅ (p˅q) ˄ (~p) ˅ F