MATEMÁTICAS DISCRETASLOGICA PROPOSICIONAL TALLER No 1 

Yeimi Carolina Acosta Ortiz – 24157Maryluz Ospina Quintero – 9866

Patricia Olmos - 10090Jonathan Jair Castro Quiñones – 9829

Omar Urazan García – 9859Rolando Cuenca -

Universidad ECCIBogotá D.CSep - 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.

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

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)

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)

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