Soal Soal Latihan Logmat

Oleh Ayu Maharani

20 tayangan
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Transkrip Soal Soal Latihan Logmat

EXERCISE

1. Justify your answers using deduction and giving the steps of your solution
in detail. Name all the rules used in your derivations.
a. Is the following reasoning correct? Translate to propositional logic and
apply inference to verify it.
“If the temperature and the pressure are constant then it does
not rain. The temperature remained constant. Thus, if it
rained, then the pressure did not remain constant.”
b. Is the following reasoning correct? Translate to propositional logic and
apply inference to verify it.
“Men eat when they are hungry. John always wears his best suit
to eat. At this moment John is not hungry. Therefore, John is
not wearing his best suit”.
2. Consider the text:
“There are only two formats for photos: round and square. Photos are either
color or black and white. Let me tell you about the photo I found
yesterday. If the photo is square, then it is a black and white picture. If
it is round, it is a digital color picture. If the photo is digital or in
black and white, then it is a portrait. If it is a portrait, then it is a
picture of my friend”
a) Build a knowledge base to represent the statements about the photo the
author of the previous text found yesterday. Use the atoms A,B,C,D,E,F,G

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Propositional Logic

b) Using inference, can you answer the author’s question: Is the photo I
found yesterday the picture of my friend?
3. Consider the text
“If the unicorn is mythical, then it is immortal, but if it is not
mythical, then it is a mortal mammal. If the unicorn is either immortal or
a mammal, then it is horned. The unicorn is magical if it is horned.”
Can we prove that the unicorn is mythical? that the unicorn is magical?
that the unicorn is horned?
4. Formalize the following arguments as syntactic sequents of the
propositional calculus, then investigate the conclusion with deduction
a. The murderer was either Colonel Mustard or Professor Plum. But it wasn’t
Professor Plum. So it was Colonel Mustard.
b. Either the Master or the Dean was in the library. But if the Master
wasn’t there,the Dean wasn’t there either. So they were both in the
library.
c. You can only buy a Young Persons railcard if you’re under 26 or a
student; otherwise not. If you can buy a Young Persons railcard, you can
get discounted train tickets. But you’re not under 26. So, unless you’re
a student, you can’t get discounted train tickets.

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d. If God is willing to prevent suffering, but unable to do so, He is not
omnipotent. If He is able to prevent suffering, but unwilling to do so,
He is not loving. If God exists, He is loving and omnipotent. And if He
is both willing and able to prevent suffering, then there can’t be any
suffering – but there is. So God doesn’t exist.
e. The protesters will go away if Oxford stops experiments on animals. But
this could only happen with government intervention. So, unless the
government intervenes, they won’t go away.
5. Here’s what you know:
Ellen is a math major or a CS major. If Ellen does not like discrete math,
she is not a CS major. If Ellen likes discrete math, she is smart. Ellen is
not a math major. Can you conclude Ellen is smart?
6. Here’s what you know:
Rainy days make gardens grow. Gardens don’t grow if it is not hot. When it
is cold outside, it rains. Prove that it’s hot.
7. Here’s what you know:
If Boris becomes a pastry chef, then if he gives in to his desire for
chocolate mousse, then his waistline will suffer.
If his waistline
suffers, then his dancing will suffer. Boris gives in to his desire for
chocolate mousse. However, his dancing will not suffer. Prove that Boris
does not become a pastry chef.
8. Formalize the following using predicate formulae
a. Anyone who doesn’t like garlic is a vampire
b. If everyone is special, no one is special
c. Everybody loves somebody.
d. Everybody loves a lover.

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Judul: Soal Soal Latihan Logmat

Oleh: Ayu Maharani


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