COS3761
EXAM PACK
,UNIVERSITY EXAMINATIONS
JUNE/JULY 2021
COS3761
Formal Logic III
Welcome to the COS3761 exam.
NB you can only download your paper from the myExams site!
To proceed with the writing of the examination, click on the link below:
https://myexams.unisa.ac.za/portal/login
Instructions:
Examination is for 100 marks. Duration of exam is 2 hours
Answer all questions.
The paper consists of 7 pages
Do all rough work in the answer book
Number your answers and label your rough work clearly
The mark for every question appears in brackets next to the question
Student should do the Honesty Declaration.
Follow the UNISA instructions for uploading your script
EXAMINATION PANEL:
First examiner: S Vallabhapurapu
Second examiner: Mr K Halland
External examiner: Dr C Dongmo
ALL THE BEST!
[TURN OVER]
, 2
COS3761
June/July 2021
QUESTION 1 [25]
Question 1.1
Consider the following propositional symbols and their intended meanings:
p : The earth is round
q: The Moon is cold
r: A lunar eclipse occurs when the
earth comes in between the sun
and the moon
(i) Express the following declarative sentence in propositional logic using the propositional symbols
as given above:
Either the earth is round or the moon is not cold (2)
(ii) Express the following propositional logic formula in English where the propositional symbols
have the meanings given above:
p (q ∨ r) (2)
Question 1.2
Use the basic natural deduction rules for propositional logic to prove the validity of the following
sequents:
(i) p → q├ ¬ p ∨ q (6)
(ii) ¬ p ∨ q├ ¬ (¬ p q) (6)
Question 1.3
Show that the following sequent is not valid by giving an appropriate valuation. (4)
p q, q ( p r) , r├ p
Explain why your valuation proves that the sequent is not valid.
[TURN OVER]
, 3
COS3761
June/July 2021
Question 1.4
Use the HORN algorithm to prove that the following Horn formula is satisfiable or not satisfiable.
Show each step.
(q r s) (q r T) (s q ) (q s r) (5)
QUESTION 2 [37]
Question 2.1
Consider the following predicate and constant symbols and their intended meanings:
S(x): x is a student in this class
C(x): x has visited Canada
E(x): x has visited Europe
(i) Express the following predicate logic formula in English, where the symbols have the meanings
as given above:
x[S(x) (C(x)∨E(x))] (3)
(ii) Express the following declarative sentence in predicate logic using the symbols as given above:
Some student in this class has visited Canada (3)
Question 2.2
Let
P be a predicate symbol with one argument and Q a predicate with two arguments, respectively
a is a constant
x, y are variables
State which of the following are well formed formulas:
(i) ∀x P(x) (1)
(ii) x Q(x, y) (1)
[TURN OVER]
EXAM PACK
,UNIVERSITY EXAMINATIONS
JUNE/JULY 2021
COS3761
Formal Logic III
Welcome to the COS3761 exam.
NB you can only download your paper from the myExams site!
To proceed with the writing of the examination, click on the link below:
https://myexams.unisa.ac.za/portal/login
Instructions:
Examination is for 100 marks. Duration of exam is 2 hours
Answer all questions.
The paper consists of 7 pages
Do all rough work in the answer book
Number your answers and label your rough work clearly
The mark for every question appears in brackets next to the question
Student should do the Honesty Declaration.
Follow the UNISA instructions for uploading your script
EXAMINATION PANEL:
First examiner: S Vallabhapurapu
Second examiner: Mr K Halland
External examiner: Dr C Dongmo
ALL THE BEST!
[TURN OVER]
, 2
COS3761
June/July 2021
QUESTION 1 [25]
Question 1.1
Consider the following propositional symbols and their intended meanings:
p : The earth is round
q: The Moon is cold
r: A lunar eclipse occurs when the
earth comes in between the sun
and the moon
(i) Express the following declarative sentence in propositional logic using the propositional symbols
as given above:
Either the earth is round or the moon is not cold (2)
(ii) Express the following propositional logic formula in English where the propositional symbols
have the meanings given above:
p (q ∨ r) (2)
Question 1.2
Use the basic natural deduction rules for propositional logic to prove the validity of the following
sequents:
(i) p → q├ ¬ p ∨ q (6)
(ii) ¬ p ∨ q├ ¬ (¬ p q) (6)
Question 1.3
Show that the following sequent is not valid by giving an appropriate valuation. (4)
p q, q ( p r) , r├ p
Explain why your valuation proves that the sequent is not valid.
[TURN OVER]
, 3
COS3761
June/July 2021
Question 1.4
Use the HORN algorithm to prove that the following Horn formula is satisfiable or not satisfiable.
Show each step.
(q r s) (q r T) (s q ) (q s r) (5)
QUESTION 2 [37]
Question 2.1
Consider the following predicate and constant symbols and their intended meanings:
S(x): x is a student in this class
C(x): x has visited Canada
E(x): x has visited Europe
(i) Express the following predicate logic formula in English, where the symbols have the meanings
as given above:
x[S(x) (C(x)∨E(x))] (3)
(ii) Express the following declarative sentence in predicate logic using the symbols as given above:
Some student in this class has visited Canada (3)
Question 2.2
Let
P be a predicate symbol with one argument and Q a predicate with two arguments, respectively
a is a constant
x, y are variables
State which of the following are well formed formulas:
(i) ∀x P(x) (1)
(ii) x Q(x, y) (1)
[TURN OVER]
