This document contains information about a workshop on propositional logic including: 1. The names of 6 students and the university where the workshop took place. 2. Several propositional logic statements and their truth tables. 3. Exercises on propositional logic including contingent statements, functional completeness, and propositional formulas.

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 - 34831
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