University of Alberta
CMPUT 272 Winter 2020
Final Examination
Time allowed: 180 minutes
(plus 15 minutes extra for uploading your files)
There are 11 questions and a total of 86 marks.
This is an OPEN BOOK exam.
You may refer to the textbook, course notes, eClass page, and the internet.
You must write the exam entirely on your own,
without any communication, hints, copying, or assistance from anyone else.
The work you submit must be your own.
Do not copy an answer from any source.
Do not share this document with anyone.
In addition to the usual properties of numbers, rules of inference, logical equivalences, defi-
nitions, and methods of proof, you may use the following facts in your proofs.
You might not need any of them.
√
2 is irrational
the product of two odd numbers is odd
positive integer powers of odd numbers are odd
the product of two even numbers is even
positive integer powers of even numbers are even
the product of an even number and an odd number is even
the sum of two odd numbers is even
the sum of two even numbers is even
every number is even or odd but not both
the 7 properties of integer division listed on page 5 of Lecture 8 notes
Good luck!
, Question 1 (8 marks) This question is about the following argument form.
f →z
z→∼o
a→s
s→ ∼z∧o
∼f →a∧∼o
∴ ∼o∧f
a) (3 marks) Explain how the truth table below shows that the argument form is valid. Be
specific and point out the relevant rows and columns in the truth table.
z f a s o f →z z→∼o a→s s→ ∼z∧o ∼f →a∧∼o ∼o∧f
1 F F F F F T T T T F F
2 F F F F T T T T T F F
3 F F F T F T T T T F F
4 F F F T T T T T T F F
5 F F T F F T T F T T F
6 F F T F T T T F T F F
7 F F T T F T T T F T F
8 F F T T T T T T T F F
9 F T F F F F T T T T T
10 F T F F T F T T T T F
11 F T F T F F T T F T T
12 F T F T T F T T T T F
13 F T T F F F T F T T T
14 F T T F T F T F T T F
15 F T T T F F T T F T T
16 F T T T T F T T T T F
17 T F F F F T T T T F F
18 T F F F T T F T T F F
19 T F F T F T T T F F F
20 T F F T T T F T F F F
21 T F T F F T T F T T F
22 T F T F T T F F T F F
23 T F T T F T T T F T F
24 T F T T T T F T F F F
25 T T F F F T T T T T T
26 T T F F T T F T T T F
27 T T F T F T T T F T T
28 T T F T T T F T F T F
29 T T T F F T T F T T T
30 T T T F T T F F T T F
31 T T T T F T T T F T T
32 T T T T T T F T F T F
2
CMPUT 272 Winter 2020
Final Examination
Time allowed: 180 minutes
(plus 15 minutes extra for uploading your files)
There are 11 questions and a total of 86 marks.
This is an OPEN BOOK exam.
You may refer to the textbook, course notes, eClass page, and the internet.
You must write the exam entirely on your own,
without any communication, hints, copying, or assistance from anyone else.
The work you submit must be your own.
Do not copy an answer from any source.
Do not share this document with anyone.
In addition to the usual properties of numbers, rules of inference, logical equivalences, defi-
nitions, and methods of proof, you may use the following facts in your proofs.
You might not need any of them.
√
2 is irrational
the product of two odd numbers is odd
positive integer powers of odd numbers are odd
the product of two even numbers is even
positive integer powers of even numbers are even
the product of an even number and an odd number is even
the sum of two odd numbers is even
the sum of two even numbers is even
every number is even or odd but not both
the 7 properties of integer division listed on page 5 of Lecture 8 notes
Good luck!
, Question 1 (8 marks) This question is about the following argument form.
f →z
z→∼o
a→s
s→ ∼z∧o
∼f →a∧∼o
∴ ∼o∧f
a) (3 marks) Explain how the truth table below shows that the argument form is valid. Be
specific and point out the relevant rows and columns in the truth table.
z f a s o f →z z→∼o a→s s→ ∼z∧o ∼f →a∧∼o ∼o∧f
1 F F F F F T T T T F F
2 F F F F T T T T T F F
3 F F F T F T T T T F F
4 F F F T T T T T T F F
5 F F T F F T T F T T F
6 F F T F T T T F T F F
7 F F T T F T T T F T F
8 F F T T T T T T T F F
9 F T F F F F T T T T T
10 F T F F T F T T T T F
11 F T F T F F T T F T T
12 F T F T T F T T T T F
13 F T T F F F T F T T T
14 F T T F T F T F T T F
15 F T T T F F T T F T T
16 F T T T T F T T T T F
17 T F F F F T T T T F F
18 T F F F T T F T T F F
19 T F F T F T T T F F F
20 T F F T T T F T F F F
21 T F T F F T T F T T F
22 T F T F T T F F T F F
23 T F T T F T T T F T F
24 T F T T T T F T F F F
25 T T F F F T T T T T T
26 T T F F T T F T T T F
27 T T F T F T T T F T T
28 T T F T T T F T F T F
29 T T T F F T T F T T T
30 T T T F T T F F T T F
31 T T T T F T T T F T T
32 T T T T T T F T F T F
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