7/23/2019 Unidad I- Segunda Parte-Enunciados y Cuantificadores

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LÓGICA MATEMÁTICA

Contenido

Proposiciones

Conectivos lógicos

Enunciado (proposición): Una proposición es una oración declarativa que es verdadera

o falsa, pero no ambas a la vez.

Ejemplo: “el oro es un metal precioso, !"#$%, !"#$& son enunciados.

Ejemplo: 'Estudia(, )Esc*c+ame, -el ibson es el mejor actor de /oll01ood no son

enunciados.

Ejemplo: Coloque 23 ejemplos de enunciados 0 23 ejemplos de e4presiones

Enunciados Preunta! opinión! e"presión e"clamati#a $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 

 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 

Tarea: -iller, C+. /eeren, 5. 6 /ornsb0, 7. 8!32#9. Matemática: Razonamiento y

 Aplicaciones. -4ico: Pearson Educación ;.<. 8Cap=tulo #> ejercicio #.2> #,%,?,@9

Consideraremos proposiciones en su forma mAs simple 8atómicas9 sin trminos de

enlace 0 las proposiciones compuestas, como aquellas formadas por proposiciones

simples mediante trminos de enlace.

Bos trminos de enlace se usan para formar nuevas proposiciones a partir de

 proposiciones atómicas.

Bos trminos de enlace 8conectores9 entre proposiciones mAs utilizados son: 0, o, no,

sientonces, si 0 solo s=.

%im&ólicamente  representaremos estos trminos de enlace por: ∧, ∨, ∼, →,↔

respectivamente.

7/23/2019 Unidad I- Segunda Parte-Enunciados y Cuantificadores

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5amos a comenzar con algunas proposiciones cu0o valor de verdad es intuitivamente

claro.

2. ;i p no es cierta, claramente ∼ p es verdadera. ;i p es cierta entonces ∼ p es falsa. 8Ba

le0 del medio e4cluido9.

!. p ∧ q es verdadera si 0 solo si ambas son verdaderas.

#. p ∨ q es verdadera si 0 solo si p es verdadera o q es verdadera.

D. Ba proposición p →  q 8p implica q9 se conoce como proposición condicional> a p

se le llama antecedente 0 a q el consecuente. ;e acostumbra con esta implicación decir 

que

 p es condición suficiente para q> q es condición necesaria para p.

%. Ba proposición p ↔  q 8p si 0 solo si q9 se conoce como proposición bicondicional

 p↔q=(q→p)∧( p→q)

Ejemplo: 'etermine si cada enunciado es compuesto %i es as identi*i+ue alconector , enci-rrelo en un crculo

a9 El Ecuador estA situado en <mrica del ;ur 0 tiene !D provincias.

 b9 Carlos da la prueba +o0 o da la prueba maana.

c9 -i pelota es de la marca Fan 0 Gus.d9 ;i el jugador de futbol Hiego -aradona es argentino entonces Ec. Iafael Correa

es el presidente de Ecuador.

e9 Jo tengo cupo en la Universidad.

Ejemplos: Hados los siguientes enunciados sepArelos de acuerdo al uso de los

conectores establecidos 0 subra0e el conector:

El presidente del Ecuador es .a*ael Correa , la ciudad de /uito es la capital del

Ecuador o 0uan 1ernando 2elasco es un cantante de reuetón

 p: El presidente del Ecuador es Iafael Correa

q: Ba ciudad de Kuito es la capital de Ecuador 

r: 7uan Lernando 5elasco es un cantante de reguetón

En la ciudad de Mana& se ela&oran artculos en paja to+uilla , Manta est3 en lareión Costa o 0ames .odrue4 es de nacionalidad 5ruua,a

s: En la ciudad de -anab= se elabora art=culos en paja toquilla

7/23/2019 Unidad I- Segunda Parte-Enunciados y Cuantificadores

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t: -anta estA en la región Costa

u: 7ames Iodr=guez es de nacionalidad Urugua0a

Taller: Escri&a cuatro proposiciones compuestas! separe los enunciados de acuerdo

al uso de los conectores esta&lecidos , su&ra,e el conector $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 

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