Matemática

“UNIVERSIDAD CENTRAL DEL ECUADOR”

FACULTAD DE FILOSOFÍA LETRAS Y CIENCIAS DE LA EDUCACIÓN

ESCUELA DE CIENCIAS EXACTAS
“INFORMÁTICA”

PROGRAMA DE EDUCACIÓN SEMIPRESENCIAL

MÓDULO: MATEMÁTICA 1
SEMESTRE: SEGUNDO
PARALELO: “B”
ESTUDIANTE: EDGAR GUAMÁN CÓRDOVA

EJERCICIOS PROPUESTOS
UNIDADES 1 - 2 - 3

24 de enero de 2009

EJERCICIOS PROPUESTOS1- LÓGICA
1. Determine el valor de verdad de los siguientes enunciados:
a.
b. 1,44 = 1,2 y 1,2 2 = 1,44
p: 1,44 = 1,2
q: 1,2 2 = 1,44
p | q | p | | q |
V | V | | V | |
V | F | | F | |
F | V | | F | |
F | F | | F | |

c. 1 m = 1O0 cm o 1 cm = 10 mm
p: 1 = 100 cm
q: 1 cm = 10 mm
p | q | p | v | q |
V | V | | V | |
V | F | | V | |F | V | | V | |
F | F | | F | |

c. Si 2 es par, entonces 22 + 1 es impar
p: Si 2 es par
q: 2 2 + 1 = es impar→
p | q | p | → | q |
V | V | | V | |
V | F | | F | |
F | V | | V | |
F | F | | V | |

d. 23= 46 , si solo si 2 x 3 ≠ 3 x 4
p: 1,44 = 1,2
q: 1,2 2 = 1,44
p | q | p | ↔ | q |
V | V | | V | |
V | F | | F | |
F | V | | F | |
F |F | | V | |

2. Utilizando tablas de verificación, determinar cuál de las siguientes proposiciones son tautologías.
d.
e. (q → s) → r
q | r | s | (q | → | s) | → | r |
V | V | V | | V | | V | |
V | V | F | | F | | V | |
V | F | V | | V | | F | |
V | F | F | | F | | V | |
F | V | V | | V | | V | |
F | V | F | | V | | V | |
F | F | V | | V| | F | |
F | F | F | | V | | F | |
No es tautología

f. p → q (q r)
p | q | r | p | → | | (q | | r) |
V | V | V | | F | F | | V | |
V | V | F | | V | V | | F | |
V | F | V | | V | V | | F | |
V | F | F | | V | V | | F | |
F | V | V | | V | F | | V | |
F | V | F | | V | V | | F | |
F | F | V | | V | V | | F | |
F | F | F | | V | V| | F | |
No es tautología

g. (r → s) (p q)
p | q | r | s | (r | → | s) | | (p | | q) |
V | V | V | V | | V | | V | | V | |
V | V | V | F | | F | | F | | V | |
V | V | F | V | | V | | V | | V | |
V | V | F | F | | V | | V | | V | |
V | F | V | V | | V | | F | | F | |
V | F | V | F | | F | | F | | F | |
V | F | F | V | | V | | F | | F| |
V | F | F | F | | V | | F | | F | |
F | V | V | V | | V | | F | | F | |
F | V | V | F | | F | | F | | F | |
F | V | F | V | | V | | F | | F | |
F | V | F | F | | V | | F | | F | |
F | F | V | V | | V | | F | | F | |
F | F | V | F | | F | | F | | F | |
F | F | V | V | | V | | F | | F | |
F | F | V | F | | F | | F | | F | |No es tautología

h. (r → q) ↔ (p ↔ r)
p | q | r | (r | → | q) | ↔ | (p | | q) |
V | V | V | | V | | V | | V | |
V | V | V | | F | | F | | V | |
V | V | F | | V | | V | | V | |
V | V | F | | V | | V | | V | |
V | F | V | | V | | F | | F | |
V | F | V | | F | | F | | F | |
V | F | F | | V | | F | | F | |
V | F | F | | V | | F | | F ||
No es tautología

i. (p → q) ↔ (p q)
p | q | | (p | → | q) | ↔ | (p | | q) |
V | V | F | | V | | V | | F | |
V | F | V | | F | | V | | V | |
F | V | F | | V | | V | | F | |
F | F | F | | V | | V | | F | |
Es tautología

j. [(p → q) (q → r)] ↔ (p → r)
p | q | r | [(p | → | q) | | (q | → | r)] | ↔ | (p | → | r) |
V | V | V | | V| | V | | V | | V | | V | |
V | V | F | | V | | F | | F | | V | | F | |
V | F | V | | F | | F | | V | | F | | V | |
V | F | F | | F | | F | | V | | V | | F | |
F | V | V | | V | | V | | V | | V | | V | |
F | V | F | | V | | F | | F | | F | | V | |
F | F | V | | V | | V | | V | | V | | V | |
F | F | F | | V | | V | | V | | V | | V | |...