Student Name: Student # __________________
Comp 3613.X1 – Artificial Intelligence December 20, 2020 1
Acadia University - Comp 3613.X1 Artificial Intelligence Dec 20, 2020

Final Examination
PLEASE READ CAREFULLY BEFORE BEGINNING

1. This Exam will start at 7pm and end at 9pm. The Exam will be available under December 20
on the ACORN course page.
2. The Exam is open book.
3. You must complete 1 question from each of the 6 Topic Sections. Each question is worth
1/6th of the over-all mark. Make sure to answer all parts of each question. If more than 1
question is answered in a Topic Section, the first one will be graded.
4. Please type in all answers to questions on this Word document (leaving the questions in place)
and include images as needed. Please keep your responses concise, but as accurate and
complete as possible. All answers must be in your own words and all drawings must be created
by your own hand. Copying from any source will be considered an infringement of
Academic Integrity.
5. When completed, please save the Word document as a PDF file with the file name
_Final_Exam.pdf.
6. You must submit your exam paper as a PDF to ACORN by 9pm in order for it to be
marked. Unless you have an accessibility accommodation, papers received after 9pm will
be marked as zero points.
7. I will be online on MS Teams for questions during the exam period. You should do the same,
so as not to miss important information that may come up during the exam period.
a. If you have a question, please put up your MS Teams hand
b. The person asking and I will enter the Students Forum, where the question can be asked
privately
c. I will share with the class any important information that comes out of such Q/A

*** In order for this exam to be marked you must sign the following declaration ***:
This exam has been completed by me, without interaction with any other human either in person or
via telecommunications.
Please print or sign your name signifying that the prior sentence is True: _____________________


Student Name: Student # __________________
Comp 3613.X1 – Artificial Intelligence December 20, 2020 2
Adversarial Search and Games

1. The games most commonly studied within AI are called two-player, turn-taking, fully
observable (perfect information), zero-sum games.
(a) Explain what zero-sum means in the context of the game of chess.
(b) List and describe the six major elements of such a game.


2. The following zero-sum game tree shows two moves by the MAX player and one move by the
MIN player. The terminal nodes show the utility values for MIN.
(a) Indicate the best values as determined by the MINIMAX algorithm for nodes A, B,
C, D, E, F and G.
(b) Which first move is best for MAX
(c) Which first move is best for MIN, given MAX moved optimally
(d) Which second move is best for MAX, given MIN moved optimally

Logical Agents

3. (a) Describe two strengths of Logical Agents and provide an example of each.
(b) Describe two weaknesses of Logical Agents and provide an example of each.


4. Which of the following are correct? Justify your answer using the definition of entailment and
the following truth table.
(a) (A ⇔ B) |= (A  B).
(b) ~(A ∨ B) |= ~A.
(c) ~(A ∧ B) |= (A ∨ B).



A
B C
D E F G
2 8 5 10 3 4 7 3 9 6
MAX
MIN
MAX
a1 a2
b2b1 c1 c2
d2d1 e1 f2d3 e2 f1 g2g1 g3
Student Name: Student # __________________
Comp 3613.X1 – Artificial Intelligence December 20, 2020 3
Propositional Logic

5. Consider the statement “if the goods are unsatisfactory, then your money will be
refunded”. This was an advertising slogan of the T. Eaton Company. This slogan can be
written as ~S ⇒ R. Is the given statement logically equivalent to:
(a) “goods satisfactory or money refunded”
(b) “if your money is not refunded, then the goods are satisfactory”
(c) “if the goods are satisfactory, then your money will not be refunded”
Show your reasoning by using propositional logic and knowledge of logically equivalence.


6. Show that the two statements (p ∧ q) ⇒ r and (p ⇒ r) ∧ (q ⇒ r) are not logically equivalent.


First Order Logic

7. Write the FOL statements that accurately convey the following:
(a) "None of my friends are perfect."
(b) “Some real numbers are rational”
(c) "All gold and silver ornaments are precious"
(d) “Every Haligonian lives in Halifax and not Dartmouth”


8. Write the English sentences that accurately capture the meaning of the following FOL
statements:
(a) ∀x love(Mary, x) ⇒ ∃y love(x,y) ∧ happy( y)
(b) ∀x cheat(x) ⇒ ∀y suffer(y)
(c) ∃x Parent(Charles, x) ∧ Male(x) ∧ [∀y Parent(Charles, y) ⇒ y=x].
(d) ∀x (run(x) ⇒ ~walk(x))


Uncertainty and Probabilistic Agents

9. A package contains 4 blue, 2 red and 3 black crayons. If 2 crayons are drawn at random from
the pack, NOT replaced and then another crayon is drawn. What is the probability of drawing 2
blue crayons followed by 1 black crayon? Please show all of your work using probabilistic
reasoning.

10. Review the full joint probability distribution shown in the table below concerning a branch
breaking off a tree as a function of wind speed and direction. Given the table values, calculate
the vector of values for the following. Please show all work for highest marks.
(a) P(WindDirection | BranchBreak = true)

Student Name: Student # __________________
Comp 3613.X1 – Artificial Intelligence December 20, 2020 4



Probabilistic and Bayesian Reasoning

11. Consider the following belief network composed of 4 random variables concerned with road
conditions, automobile accidents, and injuries on the road requiring medical assistance.
Let L = Low Visibility, W = Wet Pavement, A = Accident, I = Injury.
(a) Calculate the probability of an accident with an injury occurring when the visibility
is good but the pavement is wet. Show your work for highest mark.
(b) Calculate the probability of the pavement being dry with good visibility and there is
no accident and no injury. Show your work for highest mark.















12. (a) Draw a Bayesian network for the following scenario: You park your car in the garage most
of the time if its raining or cold. Your car gets wet if it is outside and it is raining or the
springler comes on. The seat of the car will be wet if the sun roof is open and the car is wet.
You do not have to provide conditional probability tables.

(b) List the variables of which “Car In Garage” is conditionally independent.







P(L=T) = 0.01
L W P(A)
T T 0.60
T F 0.30
F T 0.10
F F 0.05
Low Visibility Wet Pavement
Accident
Injury
P(W=T) = 0.20
A P(I)
T 0.70
F 0.001


Student Name: Student # __________________
Comp 3613.X1 – Artificial Intelligence December 20, 2020 5


BONUS QUESTION – can be done for extra points or to replace one of your 6 questions:

A sign posted outside of Halifax says “In order to attack the city, you must be green and related to
Godzilla. If you are not green and not related to Godzilla, then you cannot attack the city”.
(a) State these sentences using propositional logic. Start with: Let “a” be the assertion
“you can attack the city”, and carry on from there.
(b) Show that the two statements on the sign are not logically equivalent, contrary to
what the author probably intended.
(c) Correct the second statement so that it is logically equivalent to the first one.