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Jonathan Castro

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

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

a.
Contingencia

b.
Contingencia

Contingencia
c.

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.

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.

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.

Taller 1

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Taller 1

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

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

3.

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.