Matemáticas Discretas

Matemáticas Discretas
Acertijos Lógicos
Departamento de Matemáticas
Grupo:
Matrı́cula:
Nombre:
[Lewis Caroll] Obtain FOL formulas corresponding to each of the following premises and conclusions. Clearly state what the
universe of discourse is and what each of the predicates stands for. For each set of premises and conclusion, show that the conclusion
follows from the given premises. Note that in some cases it may be necessary to explicitly include some of the implied premises.
For example, in (1) the premise “all babies are persons” is implied. In (8), the premise “all computer romances are books” is
implied.
1. H1 : Babies are illogical.
H2 : Nobody who can manage a crocodile is despised.
H3 : Illogical persons are despised.
C : Babies cannot manage crocodiles.
Predicados:
Universo de los predicados = U = Conjunto de todas las personas.
B(x) = x es bebé.
I(x) = x es ilógico.
C(x) = x puede manejar un cocodrilo.
D(x) = x es despistado.
Reescritura de hipótesis y conclusión:
H1
H2
H3
C
:
:
:
:
∀x, B(x) → I(x)
¬ (∃x, C(x) ∧ D(x))
∀x, I(x) → D(x)
∀x, B(x) → ¬C(x)
2. H1 : Everyone who is sane can do logic.
H2 : No lunatics are fit to serve on a jury.
H3 : None of your sons can do logic.
C : None of your sons is fit to serve on a jury.
Predicados:
Universo de los predicados = U = Conjunto de todas las personas.
C(x) = x es cuerdo.
P (x) = x puede hacer Lógica.
L(x) = x es un lunático.
J(x) = x puede servir en un jurado.
H(x) = x es uno de tus hijos.
Reescritura de hipótesis y conclusión:
H1
H2
H3
C
:
:
:
:
∀x, C(x) → P (x)
¬ (∃x, L(x) ∧ J(x))
¬∃x, H(x) ∧ ¬L(x)
¬∃x, H(x) ∧ J(x)
3. H1 : Showy talkers think too much of themselves.
H2 : No really well informed people are bad company.
TC1003, Acertijos Lógicos
H3 : People who think too much of themselves are not good company.
C : Showy talkers are not really well informed.
4. H1 : Colored flowers are always scented.
H2 : I dislike flowers that are not grown outdoors.
H3 :No flowers grown outdoors are colorless.
C : No scentless flowers please me.
5. H1 : All deserts are nice.
H2 : This dish is a desert.
H3 : No nice things are wholesome.
C : This dish is not wholesome.
6. H1 : No one who is uneducated buys the New York Times.
H2 : No monkeys can read.
H3 : Those who cannot read are uneducated.
C : No monkeys buy the New York times.
7. H1 : All humming birds are richly colored.
H2 : No large birds live on honey.
H3 : Birds that do not live on honey are dull in color.
C : All humming birds are small.
8. H1 : The only books I do not recommend reading are bad.
H2 : The bound books are all well written.
H3 : All the computer romances are good.
H4 : I do not recommend you to read any of the unbound books.
C : All the computer romances are well written.
9. H1 : No interesting poems are unpopular among people of real taste.
H2 : No modern poetry is free from affectation.
H3 : All your poems are on the subject of soap bubbles.
H4 : No affected poetry is popular among people of real taste.
H5 : No ancient poem is on the subject of soap bubbles.
C : All your poems are uninteresting.
10. H1 : All writers who understand human nature are clever.
H2 : No one is a true poet unless he can stir the hearts of men.
H3 : Shakespeare wrote Hamlet.
H4 : No writer who does not understand human nature can stir the hearts of men.
H5 : None but a true poet could have written Hamlet.
C : Shakespeare was clever. -1
11. H1 : When I work a logic example without grumbling, you may be sure that it is one that I understand.
H2 : These problems are not arranged in proper order, like the ones I am used to.
H3 : No easy problem makes my headache.
H4 : I can’t understand problems that aren’t arranged in proper order, like those I am used to.
H5 : I never grumble at a problem unless it gives me a headache.
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TC1003, Acertijos Lógicos
C : These problems are difficult.
12. H1 : No husband who is always giving his wife new dresses can be an honest man.
H2 : A methodical husband always comes home for his supper.
H3 : No one who leaves his hat on the TV can be a man who is kept in proper order by his wife.
H4 : A good husband is always giving his wife new dresses.
H5 : No husband can fail to be honest if his wife does not keep him in proper order.
H6 : An unmethodical husband always leaves his hat on the TV.
C : A good husband always comes home for supper.
13. H1 : The only animals in this house are cats.
H2 : Every animal that loves to gaze at the moon is suitable for a pet.
H3 : When I detest an animal, I avoid it.
H4 : No animals are carniverous unless they prowl at night.
H5 : No cat fails to kill mice.
H6 : No animals take to me except what are in the house.
H7 : Kangaroos are not suitable as pets.
H8 : None but carnivora kill mice.
H9 : I detest animals that do not take to me.
H1 0 : Animals that prowl at night always love to gaze at the moon.
C : I always avoid a kangaroo.
http://www.math.hawaii.edu/ hile/math100/logice.htm
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