Logica proposicional taller 1
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Transcript of Logica proposicional taller 1
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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 - 34831
Universidad ECCIBogotá D.CSep - 2015
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•P ˅ q →˜r•P ˄ q →˜ (p ˄ r)•˜ p → ˜ r
LOGICA PROPOSICIONAL
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a.
Contingencia
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b.
Contingencia
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Contingencia
c.
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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.
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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.
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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.
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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
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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)
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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)
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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