unidad i- segunda parte-enunciados y cuantificadores
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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 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$