,UNIVERSITY EXAMINATIONS
January/February 2026
COS3761
Formal Logic III
100 Marks
2 Hours 15 Min
Instructions:
• Answer all questions.
• The paper consists of 7 pages. Do all rough work in the
answer book
• IRIS invigilation tool is used for the exam
• Number your answers and label your rough work clearly
• The mark for every question appears in brackets next to the
question
• Student should complete 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 Chunling Du
ALL THE BEST!
QUESTION 1
[25]
Question 1.1
Consider the following propositional symbols and their
intended meanings:
p : It is sunny
q: I am walking
, r: I will use sunscreen lotion s: I will
take a taxi
(i) Express the following declarative sentence in
propositional logic using the propositional symbols as
given above:
If it is sunny and I am walking, then I will either use
sunscreen lotion or I will take a taxi. (2)
(ii) Express the following propositional logic formula in
English where the propositional symbols have the
meanings given above:
( r ∨ s) ∧ ¬ ( r ∧ s ) (2)
Question 1.2
Use the basic natural deduction rules for propositional logic
to prove the validity of the following sequents:
(i) (p →q) ∧ (r → s)├ (p ∨ r) → ( q ∨ s)
(9)
(ii) (p →(q→r)) ├ (p ∧ q)→r
(7) Question 1.3
January/February 2026
COS3761
Formal Logic III
100 Marks
2 Hours 15 Min
Instructions:
• Answer all questions.
• The paper consists of 7 pages. Do all rough work in the
answer book
• IRIS invigilation tool is used for the exam
• Number your answers and label your rough work clearly
• The mark for every question appears in brackets next to the
question
• Student should complete 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 Chunling Du
ALL THE BEST!
QUESTION 1
[25]
Question 1.1
Consider the following propositional symbols and their
intended meanings:
p : It is sunny
q: I am walking
, r: I will use sunscreen lotion s: I will
take a taxi
(i) Express the following declarative sentence in
propositional logic using the propositional symbols as
given above:
If it is sunny and I am walking, then I will either use
sunscreen lotion or I will take a taxi. (2)
(ii) Express the following propositional logic formula in
English where the propositional symbols have the
meanings given above:
( r ∨ s) ∧ ¬ ( r ∧ s ) (2)
Question 1.2
Use the basic natural deduction rules for propositional logic
to prove the validity of the following sequents:
(i) (p →q) ∧ (r → s)├ (p ∨ r) → ( q ∨ s)
(9)
(ii) (p →(q→r)) ├ (p ∧ q)→r
(7) Question 1.3
