This document contains notes from a discrete mathematics workshop held in September 2015 at Universidad ECCI in Bogota, Colombia. It covers propositional logic, including contingencies and normal forms such as conjunctive normal form (CNF) and disjunctive normal form (DNF). Examples are provided of representing logical statements in CNF and DNF with multiple variables.

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

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.