CSE2309/3309 - CSC2091/3091 Assignment 3
CSE2309/3309 - CSC2091/3091 – Artificial Intelligence
Assignment 3 1999
Due date: 12 noon, Friday 24th September. (Submission box outside general office)
This assignment is worth 10% of your final mark for this subject. You should complete this written
assignment on your own. Please write clearly and legibly. For all questions where you are asked to
prove something, indicate what symbols stand for (as in Question 1), show the axioms you construct
from the given information and the steps you use in your proof. For the FOPC examples, show any
substitutions. Note that Q1-5 involve only propositional logic, while Q6-10 involve FOPC.
Question 1
(5 marks)
Symbolize the following sentences about the performance of the French, German, and Danish teams in
the next Olympics, using the following:
F: The French team will win at least one gold medal.
G: The German team will win at least one gold medal.
D: The Danish team will win at least one gold medal.
P: The French team is plagued with injuries.
S: The star German runner is disqualified.
R: It rains during most of the competition.
a. At least one (of the three teams) will win a gold medal.
b. At most one of them will win a gold medal.
c. Exactly one of them will win a gold medal.
d. Provided it doesn't rain during most of the competition and their star runner isn't disqualified,
the Germans will win a gold medal if either of the other teams does.
e. The Germans will win a gold medal only if it doesn't rain during most of the competition and
their star runner is not disqualified.
Question 2
(4 marks)
Look at the following sentences and decide if each is valid, unsatisfiable, or neither. Verify your
decisions using truth tables or proofs.
a. (Smoke  Fire)  (Smoke  Fire)
b.
Smoke  Fire  Fire
c. ((Smoke  Heat)  Fire)  ((Smoke  Fire)  (Heat  Fire))
d.  ((Smoke  Fire)  ((Smoke  Heat)  Fire))
Hint: A sentence is valid if you can prove it. It is unsatisfiable if its negation is valid. If it's neither you
can find an assignment of truth values that makes it false, and another which makes the sentence true.
Question 3
(8 marks)
If the rain continues, then the river rises. If rain continues and the river rises, then the bridge will wash
out. If continuation of rain will wash the bridge out, then a single road is not sufficient for the town.
Either a single road is sufficient for the town or the traffic engineers have made a mistake. Prove the
traffic engineers have made a mistake. (Hint: you should need only 4 axioms)
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CSE2309/3309 - CSC2091/3091 Assignment 3
Question 4
(8 marks)
If Mr. Smith is the brakeman's next-door neighbor, then Mr. Smith lives halfway between Detroit and
Chicago. If Mr. Smith lives halfway between Detroit and Chicago, then he does not live in Chicago. Mr.
Smith is the brakeman's next-door neighbor. If Mr. Robinson lives in Detroit, then he does not live in
Chicago. Mr. Robinson lives in Detroit. Mr. Smith lives in Chicago or else either Mr. Robinson or Mr.
Jones lives in Chicago. If Mr. Jones lives in Chicago, then the brakeman is Jones. Prove the brakeman is
Jones. (Hint: you should need only 7 axioms)
Question 5
(6 marks)
Show by a resolution refutation that the following formulas is a tautology:
(P  Q)  [(R v P)  (R v Q)]
Hint: convert the negated sentence into clausal form, then perform resolution until the nil clause in
inferred, indicating a contradiction.
Question 6
(7 marks)
Represent the following English sentences using predicate calculus:
(a) Every chicken hatched from an egg.
(b) Someone profited from the Great Depression.
(c) Some language is spoken by everyone in this room.
(d) One of the coats in the closet belongs to Sarah.
(e) All people are created equal.
(f) Everybody loves somebody sometime.
(g) An apple a day keeps the doctor away.
Question 7
(8 marks)
Prove the validity of the following wff using the method of resolution refutation:
((x)(y){[P(f(x))  Q(f(B))]  [P(f(A))  P(y)  Q(y)]}
Question 8
(8 marks)
Prove using resolution refutation that Fido will die, given the axioms:
1. Fido is a dog.
2. All dogs are animals.
3. All animals will dies.
Question 9
(8 marks)
Consider the following story of the "lucky student".
Anyone passing his or her CSE1303 exam and winning the lottery is happy. But anyone who studies or
is lucky can pass all his or her exams. Mary did not sutdy but she is lucky. Anyone who is lucky wins
the lottery. Is Mary happy? Use resolution refutation to prove your answer.
Question 10
(8 marks)
All people who are not poor and are smart are happy. Those people who read are not stupid. John can
read and is wealthy. Happy people have exciting lives. Can anyone be found with an exciting life? Use
resolution refutation to prove your answer.
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