UNISA · BSc COMPUTING · COS3761
COS3761
Formal Logic III
Past Papers with Worked Solutions
Question-by-question memo for each sitting, 2020 – 2026
with full-size Kripke models, parse trees and Fitch proofs
Eleven sittings: May/June 2020 – January/February 2026 · compiled October 2026
Companion to the “Master Exam Preparation Bible”.
UNOFFICIAL solutions: no UNISA memorandum was supplied. Every answer is an original derivation;
proofs, models and evaluations were verified by program. Not an official UNISA document.
,COS3761 Formal Logic III — Past Papers with Worked Solutions Contents
Contents
About this memo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
May/June 2020 (MJ20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
MJ20 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 5
MJ20 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . .7
MJ20 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
June/July 2021 (JJ21) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
JJ21 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 14
JJ21 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 16
JJ21 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
October/November 2021 (ON21) . . . . . . . . . . . . . . . . . . . . . . . . . 22
ON21 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 22
ON21 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 24
ON21 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
October/November 2022 (ON22) . . . . . . . . . . . . . . . . . . . . . . . . . 30
ON22 – Question 1 – Propositional logic: 28 marks printed . . . . . . . . . . . . . . . . . . . . . . . 30
ON22 – Question 2 – Predicate logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 32
ON22 – Question 3 – Modal logic: 34 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
January/February 2023 (JF23) . . . . . . . . . . . . . . . . . . . . . . . . . . 38
JF23 – Question 1 – Propositional logic: 27 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 38
JF23 – Question 2 – Predicate logic: 35 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 40
JF23 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
October/November 2023 (ON23) . . . . . . . . . . . . . . . . . . . . . . . . . 46
ON23 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 46
ON23 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 48
ON23 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
January/February 2024 (JF24) . . . . . . . . . . . . . . . . . . . . . . . . . . 54
JF24 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 54
JF24 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 56
JF24 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
October/November 2024 (ON24) . . . . . . . . . . . . . . . . . . . . . . . . . 63
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 2 of 94
,COS3761 Formal Logic III — Past Papers with Worked Solutions Contents
ON24 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 63
ON24 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 65
ON24 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
January/February 2025 (JF25) . . . . . . . . . . . . . . . . . . . . . . . . . . 71
JF25 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 71
JF25 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 73
JF25 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
October/November 2025 (ON25) . . . . . . . . . . . . . . . . . . . . . . . . . 79
ON25 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 79
ON25 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 81
ON25 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
January/February 2026 (JF26) . . . . . . . . . . . . . . . . . . . . . . . . . . 87
JF26 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 87
JF26 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 89
JF26 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 3 of 94
, COS3761 Formal Logic III — Past Papers with Worked Solutions About this memo
About this memo
For each of the eleven sittings, in paper order, you get every question part with its marks, the question as
printed (symbols normalised), and a full worked solution. Kripke models are drawn full size with the
evaluated world highlighted; parse trees colour free and bound occurrences; proofs are Fitch diagrams
with rule and line references.
KEY RULE
This is not an official UNISA memorandum. No memo was supplied with the papers. All solutions
are my own derivations. Every proof, Kripke evaluation, counter-model, HORN run and finite model was
checked by program; translations and “readings of □” are reasoned answers that a marker may word
differently.
• Where the printed paper is faulty (missing brackets, undeclared symbols, wrong word), a source
anomaly box says what is wrong and which reading was answered.
• A question repeated in several sittings is solved once and shown again in each sitting (“also set in …”).
• Marks are those printed beside each question part; Jan/Feb 2025 Q3 part-marks add to 37 against a
printed 38 (as printed); Oct/Nov 2025 Q1.1(i) has no printed mark (2 inferred).
• Jan/Feb 2025 is an image-only scan read visually; check its formulas against your copy.
• The mock papers in the source PDF are not included here; they are audited in the Master Exam
Preparation Bible (Part IV.4).
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 4 of 94
COS3761
Formal Logic III
Past Papers with Worked Solutions
Question-by-question memo for each sitting, 2020 – 2026
with full-size Kripke models, parse trees and Fitch proofs
Eleven sittings: May/June 2020 – January/February 2026 · compiled October 2026
Companion to the “Master Exam Preparation Bible”.
UNOFFICIAL solutions: no UNISA memorandum was supplied. Every answer is an original derivation;
proofs, models and evaluations were verified by program. Not an official UNISA document.
,COS3761 Formal Logic III — Past Papers with Worked Solutions Contents
Contents
About this memo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
May/June 2020 (MJ20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
MJ20 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 5
MJ20 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . .7
MJ20 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
June/July 2021 (JJ21) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
JJ21 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 14
JJ21 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 16
JJ21 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
October/November 2021 (ON21) . . . . . . . . . . . . . . . . . . . . . . . . . 22
ON21 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 22
ON21 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 24
ON21 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
October/November 2022 (ON22) . . . . . . . . . . . . . . . . . . . . . . . . . 30
ON22 – Question 1 – Propositional logic: 28 marks printed . . . . . . . . . . . . . . . . . . . . . . . 30
ON22 – Question 2 – Predicate logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 32
ON22 – Question 3 – Modal logic: 34 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
January/February 2023 (JF23) . . . . . . . . . . . . . . . . . . . . . . . . . . 38
JF23 – Question 1 – Propositional logic: 27 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 38
JF23 – Question 2 – Predicate logic: 35 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 40
JF23 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
October/November 2023 (ON23) . . . . . . . . . . . . . . . . . . . . . . . . . 46
ON23 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 46
ON23 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 48
ON23 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
January/February 2024 (JF24) . . . . . . . . . . . . . . . . . . . . . . . . . . 54
JF24 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 54
JF24 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 56
JF24 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
October/November 2024 (ON24) . . . . . . . . . . . . . . . . . . . . . . . . . 63
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 2 of 94
,COS3761 Formal Logic III — Past Papers with Worked Solutions Contents
ON24 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 63
ON24 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 65
ON24 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
January/February 2025 (JF25) . . . . . . . . . . . . . . . . . . . . . . . . . . 71
JF25 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 71
JF25 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 73
JF25 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
October/November 2025 (ON25) . . . . . . . . . . . . . . . . . . . . . . . . . 79
ON25 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . 79
ON25 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . 81
ON25 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
January/February 2026 (JF26) . . . . . . . . . . . . . . . . . . . . . . . . . . 87
JF26 – Question 1 – Propositional logic: 25 marks printed . . . . . . . . . . . . . . . . . . . . . . . . 87
JF26 – Question 2 – Predicate logic: 37 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . 89
JF26 – Question 3 – Modal logic: 38 marks printed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 3 of 94
, COS3761 Formal Logic III — Past Papers with Worked Solutions About this memo
About this memo
For each of the eleven sittings, in paper order, you get every question part with its marks, the question as
printed (symbols normalised), and a full worked solution. Kripke models are drawn full size with the
evaluated world highlighted; parse trees colour free and bound occurrences; proofs are Fitch diagrams
with rule and line references.
KEY RULE
This is not an official UNISA memorandum. No memo was supplied with the papers. All solutions
are my own derivations. Every proof, Kripke evaluation, counter-model, HORN run and finite model was
checked by program; translations and “readings of □” are reasoned answers that a marker may word
differently.
• Where the printed paper is faulty (missing brackets, undeclared symbols, wrong word), a source
anomaly box says what is wrong and which reading was answered.
• A question repeated in several sittings is solved once and shown again in each sitting (“also set in …”).
• Marks are those printed beside each question part; Jan/Feb 2025 Q3 part-marks add to 37 against a
printed 38 (as printed); Oct/Nov 2025 Q1.1(i) has no printed mark (2 inferred).
• Jan/Feb 2025 is an image-only scan read visually; check its formulas against your copy.
• The mock papers in the source PDF are not included here; they are audited in the Master Exam
Preparation Bible (Part IV.4).
Unofficial solutions · no UNISA memorandum supplied · compiled October 2026 Page 4 of 94
